deco polyominoes permutations and random generation abstract in this paper we introduce a class of polyominoes called deco polyominoes in bijection with the set of permutations of the first k integers we evaluate some typical parameters for this class of polyominoes and define a linear algorithm for randomly generating them moreover we define the polyominoes corresponding to the directed animals on the hexagonal and triangular lattices and examine these polyominoes deco class as far as deco polyominoes corresponding to animals on the hexagonal lattice are concerned we find a bijection with a class of permutations finally we give linear algorithms for randomly generating both hexagonal and triangular deco polyominoes

low density series expansions for directed percolation on square and triangular lattices greatly extended series have been derived for moments of the pair connectedness for bond and site percolation on the directed square and triangular lattices the length of the various series has been at least doubled to more than 110 100 terms for the square lattice bond site problem and more than 55 terms for the bond and site problems on the triangular lattice analysis of the series leads to very accurate estimates for the critical parameters and generally seems to rule out simple rational values for the critical exponents the values of the critical exponents for the average cluster size parallel and perpendicular connectedness lengths are estimated by d 2 277 69 4 k d 1 733 825 25 and d 1 096 844 14 respectively an improved estimate for the percolation probability exponent is obtained from the scaling relation d k c 2 d 0 276 49 4 in all cases the leading correction to scaling term is analytic

an exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts this paper presents a new exact algorithm for the capacitated vehicle routing problem cvrp based on the set partitioning formulation with additional cuts that correspond to capacity and clique inequalities the exact algorithm uses a bounding procedure that finds a near optimal dual solution of the lp relaxation of the resulting mathematical formulation by combining three dual ascent heuristics the first dual heuristic is based on the q route relaxation of the set partitioning formulation of the cvrp the second one combines lagrangean relaxation pricing and cut generation the third attempts to close the duality gap left by the first two procedures using a classical pricing and cut generation technique the final dual solution is used to generate a reduced problem containing only the routes whose reduced costs are smaller than the gap between an upper bound and the lower bound achieved the resulting problem is solved by an integer programming solver computational results over the main instances from the literature show the effectiveness of the proposed algorithm

an exact algorithm for the capacitated vehicle routing problem based on a two commodity network flow formulation the capacitated vehicle routing problem cvrp is the problem in which a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints in this paper we describe a new integer programming formulation for the cvrp based on a two commodity network flow approach we present a lower bound derived from the linear programming lp relaxation of the new formulation which is improved by adding valid inequalities in a cutting plane fashion moreover we present a comparison between the new lower bound and lower bounds derived from the lp relaxations of different cvrp formulations proposed in the literature a new branch and cut algorithm for the optimal solution of the cvrp is described computational results are reported for a set of test problems derived from the literature and for new randomly generated problems

semismooth newton method for frictional contact between pseudo rigid bodies recently developed semismooth newton approach is adopted in the context of the frictional contact between three dimensional pseudo rigid bodies the signorini coulomb problem is formulated according to the formalism of the contact dynamics method hybrid linearisation penalty scaling and line search techniques are combined as the global convergence enhancements of the newton algorithm quasi static simulations of dry masonry assemblies exemplify performance of the presented framework

a new two variable generating function for convex self avoiding polygons the width of a self avoiding polygon on the square lattice is defined as the minimal horizontal or vertical distance between two of its parallel edges if the polygons are convex this distance is internal the perimeter generating functions for such convex polygons whose widths exceed a threshold can be given explicitly from these expressions a two variable width and perimeter generating function can be constructed the corresponding phase diagram shows two types of critical behaviour which meet at a tricritical point

convex polyominoes and heaps of segments builds a one to one correspondence between some polyominoes called parallelogram polyominoes and some heaps of segments then the author derives explicit expressions for the generating function of convex polyominoes according to their height width and area the author also enumerates two subsets of convex polyominoes namely the directed and convex polyominoes and the parallelogram polyominoes according to these three parameters generating functions of polyominoes having a fixed width are also studied

a unified solution framework for multi attribute vehicle routing problems vehicle routing attributes are extra characteristics and decisions that complement the academic problem formulations and aim to properly account for real life application needs hundreds of methods have been introduced in recent years for specific attributes but the development of a single general purpose algorithm which is both efficient and applicable to a wide family of variants remains a considerable challenge yet such a development is critical for understanding the proper impact of attributes on resolution approaches and to answer the needs of actual applications this paper contributes towards addressing these challenges with a component based design for heuristics targeting multi attribute vehicle routing problems and an efficient general purpose solver the proposed unified hybrid genetic search metaheuristic relies on problem independent unified local search genetic operators and advanced diversity management methods problem specifics are confined to a limited part of the method and are addressed by means of assignment sequencing and route evaluation components which are automatically selected and adapted and provide the fundamental operators to manage attribute specificities extensive computational experiments on 29 prominent vehicle routing variants 42 benchmark instance sets and overall 1099 instances demonstrate the remarkable performance of the method which matches or outperforms the current state of the art problem tailored algorithms thus generality does not necessarily go against efficiency for these problem classes

number of almost convex polygons on the square lattice the generating function for the number nc n of almost convex polygons on the square lattice with concavity index c 1 and perimeter n is derived rigorously the asymptotic behaviour of nc n for large n is determined and this result confirms a conjecture by enting et al 1992

numerical aspects of non smooth multibody dynamics the theory of non smooth multibody dynamics with unilateral contacts is now well established for example in terms of measure equations of motion added by complementarities or formulated with the help of differential inclusions most researchers today focus on numerical methods for solving these systems because computing times especially for large systems are a problem time stepping schemes for time integration pivoting or iterative algorithms for solving the complementarity problem and the augmented lagrangian approach are methods of increasing numerical efficiency for large systems the paper describes new findings for unilateral multibody systems and discusses two large industrial examples namely the dynamics of a roller coaster and the behavior of a drop tower featuring hydraulic components

the complexity of computing the number of strings of given length in context free languages abstract computing the number of strings of given length contained in a language is related to classical problems of combinatorics formal languages and computational complexity here we study the complexity of this problem in the case of context free languages it is shown that for unambiguous context free languages such a computation is easy and can be carried out by efficient parallel algorithms on the contrary for some context free languages of ambiguity degree two the problem becomes intractable these results are related to other classical subjects concerning counting problems exponential time recognizable languages and sparse sets

a reliable algorithm to solve 3d frictional multi contact problems application to granular media we present in this paper an improved non smooth discrete element method dem in 3d based on the non smooth contact dynamics nscd method we consider a three dimensional collection of rigid particles spheres during the motion of which contacts can occur or break the dry friction is modeled by coulomb s law which is typically non associated the non associativity of the constitutive law poses numerical challenges by adopting the use of the bi potential concept in the framework of the nscd dem a faster and more robust time stepping algorithm with only one predictor corrector step where the contact and the friction are coupled can be devised this contrasts with the classical method where contact and friction are treated separately leading to a time stepping algorithm that involves two predictor corrector steps the algorithm has been introduced in a 3d version of the nscd dem software multicor numerical applications will show the robustness of the algorithm and the possibilities of the multicor software for solving three dimensional problems

exact algorithms for the vehicle routing problem based on spanning tree and shortest path relaxations we consider the problem of routing vehicles stationed at a central facility depot to supply customers with known demands in such a way as to minimize the total distance travelled the problem is referred to as the vehicle routing problem vrp and is a generalization of the multiple travelling salesman problem that has many practical applications we present tree search algorithms for the exact solution of the vrp incorporating lower bounds computed from i shortest spanning k degree centre tree k dct and ii q routes the final algorithms also include problem reduction and dominance tests computational results are presented for a number of problems derived from the literature the results show that the bounds derived from the q routes are superior to those from k dct and that vrps of up to about 25 customers can be solved exactly

an integrative cooperative search framework for multi decision attribute combinatorial optimization application to the mdpvrp abstract we introduce the integrative cooperative search method ics a multi thread cooperative search method for multi attribute combinatorial optimization problems ics musters the combined capabilities of a number of independent exact or meta heuristic solution methods a number of these methods work on sub problems defined by suitably selected subsets of decision set attributes of the problem while others combine the resulting partial solutions into complete ones and eventually improve them all these methods cooperate through an adaptive search guidance mechanism using the central memory cooperative search paradigm extensive numerical experiments explore the behavior of ics and its interest through an application to the multi depot periodic vehicle routing problem for which ics improves the results of the current state of the art methods

rigorous derivation of the perimeter generating function for the mean squared radius of gyration of convex polygons we have rigorously derived the perimeter generating function for the mean squared radius of gyration of convex polygons this function was first conjectured by jensen his nonrigorous result is based on the analysis of the long series expansions

area weighted moments of convex polygons on the square lattice when constructing series expansions for the zero field partition function of the q state potts model on the square lattice using the finite lattice method the series can be extended by one term by adding a correction of q 1 times the number of convex polygons of an appropriate order by virtue of duality such corrections apply for both high and low temperature series for low temperature series corrections to the field dependent partition function are of the same order in the temperature variable as the zero field correction the general corrections are given by area weighted moments of the number of convex polygons the authors obtain conjectured closed form expressions for the two generating functions that give corrections to the first two field derivatives of the low temperature partition function

directed compact percolation near a wall iii exact results for the mean length and number of contacts existing exact results for the percolation probability and mean cluster size for compact percolation near a dry wall are extended to the mean cluster length and the mean number of contacts with the wall the results are derived from our previous work on vesicles near an attractive wall and involve elliptic integrals as opposed to the simple rational forms found for the percolation probability and cluster size below the results for the cluster length satisfy previously conjectured differential equations a closed expression is conjectured for the mean size above in terms of a hypergeometric function

exact solution of the convex polygon perimeter and area generating function an explicit expression is derived for the three variable generating function p x y z sigma m or 1 sigma n or 1 sigma r or 1 x2ny2mzrcn m r where cn m r is the number of convex polygons with horizontal width n vertical height m and area r

time integrators based on approximate discontinuous hamiltonians summary we introduce a class of time integration algorithms for finite dimensional mechanical systems whose hamiltonians are separable by partitioning the system s configuration space to construct an approximate potential energy we define an approximate discontinuous hamiltonian adh whose resulting equations of motion can be solved exactly the resulting integrators are symplectic and precisely conserve the approximate energy which by design is always close to the exact one we then propose two adh algorithms for finite element discretizations of nonlinear elastic bodies these result in two classes of explicit asynchronous time integrators that are scalable and because they conserve the approximate hamiltonian could be considered to be unconditionally stable in some circumstances in addition these integrators can naturally incorporate frictionless contact conditions we discuss the momentum conservation properties of the resulting methods and demonstrate their performance with several problems such as rotating bodies and multiple collisions of bodies with rigid boundaries copyright 2011 john wiley sons ltd

strip tiling and regular grammars we study the problem of tiling a rectangular p n strip fixed with pieces i e sets of simply connected cells some well known examples are strip tilings with dimers dominoes and or monomers we prove in a constructive way that every tiling problem is equivalent to a regular grammar that is the set of possible tilings constitutes a regular language we propose a straightforward algorithm to transform the tiling problem into its corresponding grammar by means of some standard methods we are then able to obtain some counting generating functions that are rational we go on to give some examples of our method and indicate some of its applications to a number of problems treated in current literature

self avoiding polygons on the square lattice we have developed an improved algorithm that allows us to enumerate the number of self avoiding polygons on the square lattice to perimeter length 90 analysis of the resulting series yields very accurate estimates of the connective constant 2 638 158 529 27 1 biased and the critical exponent 0 500 0005 10 unbiased the critical point is indistinguishable from a root of the polynomial 581x4 7x2 13 0 an asymptotic expansion for the coefficients is given for all n there is strong evidence for the absence of any non analytic correction to scaling exponent

modeling for dynamics of rigid body systems with friction by linear complementary problem lcp the purpose of this paper is to study the modeling method for nonholonomic systems with friction by linear complementary problem lcp firstly the dynamic equation with multipliers for the nonholonomic system with friction is given secondly a standard linear complementary model is established which describes the normal and tangential characteristics for a nonholonomic system thirdly by using lcp theory a general criterion is obtained which can identify the singularity induced by nonideal geometrical constraints in a nonholonomic system by a typical example of a nonholonomic system with friction it is revealed how the problem solving for the constraint reaction forces can be transformed into the standard linear complementary problem the research work may provide reliable theoretical basis for the dynamical simulation of a nonholonomic system with non smooth factors

enumeration of polyominoes using macsyma this paper shows the use of a symbolic language macsyma to obtain new exact or asymptotic results in combinatorics the examples are taken among polyominoes sic objects the main purpose of the paper is to show how easy it is to bring some methods into operation in order to obtain new results in enumerative combinatorics from the abstract

generating functions for classes of self avoiding polygons on the square lattice abstract a transfer matrix technique is presented which allows the explicit calculation of the generating functions for those self avoiding polygons on the square lattice which have a perimeter equal to or two larger than the perimeter of their bounding rectangles

unidirectional convex polygons on the honeycomb lattice the authors obtain the exact generating function for a class of self avoiding polygons on the honeycomb lattice which are convex in one of the three lattice directions it is shown that the critical exponent alpha of these unidirectional convex polygons is 3 2

convex polyominoes and algebraic languages uses the so called dsv methodology that links some enumeration problems to the theory of algebraic languages to get a system of q difference equations involving the generating functions of convex polyominoes of convex and directed polyominoes and of parallelogram polyominoes according to their height width and area then the author shows various applications of this system

on modified runge kutta trees and methods modifled runge kutta mrk methods can have interesting properties as their coe cients may depend on the step length by a simple perturbation of very few coe cients we may produce various function fltted methods and avoid the overload of evaluating all the coe cients in every step it is known that for runge kutta methods each order condition corresponds to a rooted tree when we expand this theory to the case of mrk methods some of the rooted trees produce additional trees called mrk rooted trees and so additional conditions of order in this work we present the relative theory including a theorem for the generating function of these additional mrk trees and explain the procedure to determine the extra algebraic equations of condition generated for a major subcategory of these methods moreover e cient symbolic codes are provided for the enumeration of the trees and the generation of the additional order conditions finally phase lag and phase fltted properties are analyzed for this case and speciflc phase fltted pairs of orders 8 6 and 6 5 are presented and tested

enumeration of 4 stack polyominoes in this paper we consider the class of 4 stack polyominoes i e polyominoes which can be decomposed into a central rectangle supporting four stack polyominoes one on each side of the rectangle this class of objects recently introduced by marc noy extends the class of centered convex polyominoes and is included into the class of z convex polyominoes using an inclusion exclusion approach we obtain the enumeration of 4 stack polyominoes according to the number of rows and columns moreover we solve some problems posed by marc noy proving that the generating function of 4 stack polyominoes according to the semi perimeter is algebraic and that their asymptotic behavior is n4 n which is immediately smaller than the asymptotic behavior of z convex polyominoes which is n4 n as a corollary of our result we find the generating function of bi centered polyominoes i e convex polyominoes which are both horizontally and vertically centered

a unified exact method for solving different classes of vehicle routing problems this paper presents a unified exact method for solving an extended model of the well known capacitated vehicle routing problem cvrp called the heterogenous vehicle routing problem hvrp where a mixed fleet of vehicles having different capacities routing and fixed costs is used to supply a set of customers the hvrp model considered in this paper contains as special cases the single depot cvrp all variants of the hvrp presented in the literature the site dependent vehicle routing problem sdvrp and the multi depot vehicle routing problem mdvrp this paper presents an exact algorithm for the hvrp based on the set partitioning formulation the exact algorithm uses three types of bounding procedures based on the lp relaxation and on the lagrangean relaxation of the mathematical formulation the bounding procedures allow to reduce the number of variables of the formulation so that the resulting problem can be solved by an integer linear programming solver extensive computational results over the main instances from the literature of the different variants of hvrps sdvrp and mdvrp show that the proposed lower bound is superior to the ones presented in the literature and that the exact algorithm can solve for the first time ever several test instances of all problem types considered

sequential and parallel large neighborhood search algorithms for the periodic location routing problem we propose a large neighborhood search lns algorithm to solve the periodic location routing problem plrp the plrp combines location and routing decisions over a planning horizon in which customers require visits according to a given frequency and the specific visit days can be chosen we use parallelization strategies that can exploit the availability of multiple processors the computational results show that the algorithms obtain better results than previous solution methods on a set of standard benchmark instances from the literature

a variable neighborhood search heuristic for periodic routing problems the aim of this paper is to propose a new heuristic for the periodic vehicle routing problem pvrp without time windows the pvrp extends the classical vehicle routing problem vrp to a planning horizon of several days each customer requires a certain number of visits within this time horizon while there is some flexibility on the exact days of the visits hence one has to choose the visit days for each customer and to solve a vrp for each day our method is based on variable neighborhood search vns computational results are presented that show that our approach is competitive and even outperforms existing solution procedures proposed in the literature also considered is the special case of a single vehicle i e the periodic traveling salesman problem ptsp it is shown that slight changes of the proposed vns procedure is also competitive for the ptsp

on an involution on dyck paths les derniers resultats concernant l enumeration des polyamines parallelogrammes 4 5 8 9 11 14 selon l aire et le nombre de colonnes font apparaitre des fonctions generatrices s exprimant comme rapport de q analogues de fonctions de bessel dans 13 deux interpretations combinatoires de ces memes fonctions sont donnees d une part en termes de multiparcours d arbres et d autre part en termes de multichaines de chemins de dyck a l aide d une involution sur l ensemble d des chemins de dyck d une bijection entre chemins et multiparcours d arbres et d une bijection entre chemins et multichaines nous donnons dans ce papier une preuve bijective de l equivalence de ces deux interpretations

event driven integration of linear structural dynamics models under unilateral elastic constraints abstract this paper proposes an algorithm for the numerical simulation of linear structural dynamics problems under unilateral elastic constraints i e constraints with a linear force displacement characteristic whenever active the presented procedure relies on an event driven strategy for the handling of the contact constraints in combination with one step schemes dedicated to the time integration of the second order equations of motion efficiency of the procedure follows from the use of cubic hermite interpolation to continuously extend the normal gap functions that reflect the openings of the contact interfaces robustness follows from the proper handling of complex numerical situations e g numerical grazing or discontinuity sticking through appropriate algorithm structure and numerical implementation and integration stability is guaranteed by the very nature of the algorithm and that of the one step integration scheme following a detailed coverage of the integration procedure and the countermeasures to the expected numerical difficulties three application examples are treated for illustration purposes a matlab implementation of the procedure is provided online download and usage information are given in appendix a

walks on the slit plane in the first part of this paper we enumerate exactly walks on the square lattice that start from the origin but otherwise avoid the half line we call them walks on the slit plane we count them by their length and by the coordinates of their endpoint the corresponding three variable is algebraic of degree 8 moreover for any point i j the length for walks of this type ending at i j is also algebraic of degree 2 or 4 and involves the famous catalan numbers

a parallel algorithm for the enumeration of self avoiding polygons on the square lattice we have developed a parallel algorithm that allows us to enumerate the number of self avoiding polygons on the square lattice to perimeter length 110 we have also extended the series for the first 10 area weighted moments and the radius of gyration to 100 analysis of the resulting series yields very accurate estimates of the connective constant 2 638 158 530 31 3 biased and the critical exponent 0 500 000 1 2 unbiased in addition we obtain very accurate estimates for the leading amplitudes confirming to a high degree of accuracy various predictions for universal amplitude combinations

context free grammars differential operators and formal power series abstract in this paper we introduce the concepts of a formal function over an alphabet and a formal derivative based on a set of substitution rules we call such a set of rules a context free grammar because these rules act like a context free grammar in the sense of a formal language given a context free grammar we can associate each formal function with an exponential formal power series in this way we obtain grammatical interpretations of addition multiplication and functional composition of formal power series a surprising fact about the grammatical calculus is that the composition of two formal power series enjoys a very simple grammatical representation we apply this method to obtain simple demonstrations of faa di bruno s formula and some identities concerning bell polynomials stirling numbers and symmetric functions in particular the lagrange inversion formula has a simple grammatical representation from this point of view one sees that cayley s formula on labeled trees is equivalent to the lagrange inversion formula

two generalizations of column convex polygons column convex polygons were first counted by area several decades ago and the result was found to be a simple rational generating function in this work we generalize that result let a p column polyomino be a polyomino whose columns can have 1 2 p connected components then column convex polygons are equivalent to 1 convex polyominoes the area generating function of even the simplest generalization namely 2 column polyominoes is unlikely to be solvable we therefore define two classes of polyominoes which interpolate between column convex polygons and 2 column polyominoes we derive the area generating functions of those two classes using extensions of existing algorithms the growth constants of both classes are greater than the growth constant of column convex polyominoes rather tight lower bounds on the growth constants complement a comprehensive asymptotic analysis

object grammars and bijections a new systematic approach for the specification of bijections between sets of combinatorial objects is presented it is based on the notion of object grammars object grammars give recursive descriptions of objects and generalize context free grammars the study of a particular substitution in these object grammars confirms once more the key role of dyck words in the domain of enumerative and bijective combinatorics

exact solution of the row convex polygon perimeter generating function an explicit expression is obtained for the perimeter generating function g y sigma n or 2 any2n for row convex polygons on the square lattice where an is the number of 2n step row convex polygons an asymptotic expression for an approximately a mu nn 3 2 is obtained where mu 3 22 and a are given the authors also show that the generating function is an algebraic function and that it satisfies an inhomogeneous linear differential equation of degree three

asymptotic matching by the symbolic manipulator macsyma abstract we consider delegating the tedious labor of calculating higher order terms in singular perturbation expansions to a computer by using the algebraic manipulation system macsyma in particular the method of matched asymptotic expansions for two model singular perturbation problems have been studied in detail the first model resembles the boundary layer equation with a small parameter multiplying the highest derivative in this case both the outer and inner expansions are simple power series in e the second model is a turning point problem the asymptotic expansions that resemble the series in low reynolds number flow past a sphere are mixtures of powers and logarithms in e and fraenkel s restricted matching principle is needed we show that macsyma has successfully performed the higher order matching in these two problems

algebraic languages and polyominoes enumeration abstract in this paper the use of algebraic languages theory in solving an open problem in combinatorics is shown by constructing a bijection between convex polyominoes and words of an algebraic language and by solving the corresponding algebraic system we prove that the number of convex polyominoes with perimeter 2n 8 is 2n 11 4 n 4 2n 1 2n n

statistical mechanics of directed models of polymers in the square lattice directed square lattice models of polymers and vesicles have received considerable attention in the recent mathematical and physical sciences literature these are idealized geometric directed lattice models introduced to study phase behaviour in polymers and include dyck paths partially directed paths directed trees and directed vesicles models directed models are closely related to models studied in the combinatorics literature and are often exactly solvable they are also simplified versions of a number of statistical mechanics models including the self avoiding walk lattice animals and lattice vesicles the exchange of approaches and ideas between statistical mechanics and combinatorics have considerably advanced the description and understanding of directed lattice models and this will be explored in this review the combinatorial nature of directed lattice path models makes a study using generating function approaches most natural in contrast the statistical mechanics approach would introduce partition functions and free energies and then investigate these using the general framework of critical phenomena generating function and statistical mechanics approaches are closely related for example questions regarding the limiting free energy may be approached by considering the radius of convergence of a generating function and the scaling properties of thermodynamic quantities are related to the asymptotic properties of the generating function in this review the methods for obtaining generating functions and determining free energies in directed lattice path models of linear polymers is presented these methods include decomposition methods leading to functional recursions as well as the temperley method that is implemented by creating a combinatorial object one slice at a time a constant term formulation of the generating function will also be reviewed the thermodynamic features and critical behaviour in models of directed paths may be informative about the underlying properties that determine phase diagrams for wider classes of models including physical models of polymers of particular interest are adsorption and collapse transitions in models of polymers and copolymers the properties of thermodynamic quantities in those models are described by tricritical scaling this is reviewed for directed path models and the generating function approaches can be used to apply tricritical scaling to models of adsorbing inflating and collapsing directed lattice paths critical exponents for a variety of models can be obtained in this manner and with it a better understanding and a classification of the models

statistics of collapsed lattice animals rigorous results and monte carlo simulations in this paper a two dimensional model of collapsed lattice animals with nearest neighbour contact interactions is introduced and the limiting free energy for the model is proved to exist we also establish that the partition function for collapsed lattice animals is related to the reliability polynomial for the m m grid graph and to the generating function for spanning forests on the m m grid graph from these relationships and using results about directed animals we are able to obtain rigorous upper and lower bounds on the free energy for collapsed lattice animals in addition we present monte carlo evidence that the heat capacity associated with this model remains bounded in the thermodynamic limit in fact we do not find any evidence for a second order phase transition for collapsed lattice animals

a strip like tiling algorithm we extend our previous results on the connection between strip tiling problems and regular grammars by showing that an analogous algorithm is applicable to other tiling problems not necessarily related to rectangular strips we find generating functions for monomer and dimer tilings of t and l shaped figures holed and slotted strips diagonal strips and combinations of them and show how analogous results can be obtained by using different pieces

runge kutta pairs of order 5 4 satisfying only the first column simplifying assumption among the most popular methods for the solution of the initial value problem are the runge kutta pairs of orders 5 and 4 these methods can be derived solving a system of nonlinear equations for its coefficients to achieve this we usually admit various simplifying assumptions the most common of them are the so called row simplifying assumptions here we neglect them and present an algorithm for the construction of runge kutta pairs of orders 5 and 4 based only in the first column simplifying assumption the result is a pair that outperforms other known pairs in the bibliography when tested to the standard set of problems of detest a cost free fourth order formula is also derived for handling dense output

a new branch and cut algorithm for the capacitated vehicle routing problem we present a new branch and cut algorithm for the capacitated vehicle routing problem cvrp the algorithm uses a variety of cutting planes including capacity framed capacity generalized capacity strengthened comb multistar partial multistar extended hypotour inequalities and classical gomory mixed integer cuts for each of these classes of inequalities we describe our separation algorithms in detail also we describe the other important ingredients of our branch and cut algorithm such as the branching rules the node selection strategy and the cut pool management computational results for a large number of instances show that the new algorithm is competitive in particular we solve three instances b n50 k8 b n66 k9 and b n78 k10 of augerat to optimality for the first time

robust branch and cut and price for the capacitated vehicle routing problem the best exact algorithms for the capacitated vehicle routing problem cvrp have been based on either branch and cut or lagrangean relaxation column generation this paper presents an algorithm that combines both approaches it works over the intersection of two polytopes one associated with a traditional lagrangean relaxation over q routes the other defined by bound degree and capacity constraints this is equivalent to a linear program with exponentially many variables and constraints that can lead to lower bounds that are superior to those given by previous methods the resulting branch and cut and price algorithm can solve to optimality all instances from the literature with up to 135 vertices this more than doubles the size of the instances that can be consistently solved

dynamic modeling and control of an octopus inspired multiple continuum arm robot this paper proposes a dynamic model for a multiple continuum arm robot inspired by live octopuses the kinematics and dynamics for a single arm are analyzed and formulated including the longitudinal muscles radial muscles isovolumetric constraints and interaction between suckers and an object the single arm model is then expanded to a multiple arm system that is capable of generating archetypal locomotion patterns such as crawling and swimming a hierarchical controller based on octopus neurophysiology is used to achieve simple and reliable control of the multiple continuum arm system simulations for single arm movements and multiple arm locomotions are presented the results of this work can be used in the study of control schemes for multiple continuum arm robots and live octopuses

an exact algorithm for the period routing problem this paper presents an exact algorithm for solving strategic and tactical multiperiod vehicle routing problems that can be modeled as period vehicle routing problems pvrps the pvrp is defined on a time horizon of several days and consists of assigning appropriate combinations of delivery to customers and designing a set of delivery routes for every day of the planning period the objective is to service all customers assigned to each day minimizing the overall routing cost this paper describes an integer programming formulation of the pvrp that is used to derive different lower bounds and an exact solution method computational results on test instances from the literature and on new sets of test instances show the effectiveness of the proposed method

the perimeter generating functions of three choice imperfect and one punctured staircase polygons we consider the isotropic perimeter generating functions of three choice imperfect and one punctured staircase polygons whose 8th order linear fuchsian odes are previously known we derive simple relationships between the three generating functions and show that all three generating functions are joint solutions of a common 12th order fuchsian linear ode we find that the 8th order differential operators can each be rewritten as a direct sum of a direct product with operators no larger than 3rd order we give closed form expressions for all the solutions of these operators in terms of 2 f 1 hypergeometric functions with rational and algebraic arguments the solutions of these linear differential operators can in fact be expressed in terms of two modular forms since these 2 f 1 hypergeometric functions can be expressed with two rational or algebraic pullbacks