bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Goldman-Rota Identity and the Grassmann Scheme
Authors: Srinivasan Murali K. 
Published: January 2020

We inductively construct an explicit (common) orthogonal eigenbasis for the elements of the Bose-Mesner algebra of the Grassmann scheme.The key step is a constructive, linear algebraic interpretation of the Goldman-Rota recurrence for the number of subspaces of a finite vector space. This interpretation shows that the up operator on subspaces has an explicitly given recursive structure. Using the interpretation above we inductively construct an explicit orthogonal symmetric Jordan basis with respect to the up operator and write down the singular values, i.e., the ratio of the lengths of the successive vectors in the Jordan chains. The collection of all vectors in this basis of a fixed rank $m$ forms a (common) orthogonal eigenbasis for the elements of the Bose-Mesner algebra of the Grassmann scheme of $m$-dimensional subspaces. We also pose a bijective proof problem on the spanning trees of the Grassmann graphs.
Extensions to 2-Factors in Bipartite Graphs
Authors: Vandenbussche Jennifer , West Douglas B. 
Published: January 2020

A graph is $d$-bounded if its maximum degree is at most $d$. We apply the Ore-Ryser Theorem on $f$-factors in bipartite graphs to obtain conditions for the extension of a $2$-bounded subgraph to a $2$-factor in a bipartite graph. As consequences, we prove that every matching in the $5$-dimensional hypercube extends to a $2$-factor, and we obtain conditions for this property in general regular bipartite graphs. For example, to show that every matching in a regular $n$-vertex bipartite graph extends to a $2$-factor, it suffices to show that all matchings with fewer than $n/3$ edges extend to $2$-factors.
Some Results on the Structure of Multipoles in the Study of Snarks
Authors: Fiol M. A. , Vilaltella J. 
Published: January 2020

Multipoles are the pieces we obtain by cutting some edges of a cubic graph in one or more points. As a result of the cut, a multipole $M$ has vertices attached to a dangling edge with one free end, and isolated edges with two free ends. We refer to such free ends as semiedges, and to isolated edges as free edges. Every 3-edge-coloring of a multipole induces a coloring or state of its semiedges, which satisfies the Parity Lemma. Multipoles have been extensively used in the study of snarks, that is, cubic graphs which are not 3-edge-colorable. Some results on the states and structure of the so-called color complete and color closed multipoles are presented. In particular, we give lower and upper linear bounds on the minimum order of a color complete multipole, and compute its exact number of states. Given two multipoles $M_1$ and $M_2$ with the same number of semiedges, we say that $M_1$ is reducible to $M_2$ if the state set of $M_2$ is a non-empty subset of the state set of $M_1$ and $M_2$ has less vertices than $M_1$. The function $v(m)$ is defined as the maximum number of vertices of an irreducible multipole with $m$ semiedges. The exact values of $v(m)$ are only known for $m\le 5$. We prove that tree and cycle multipoles are irreducible and, as a byproduct, that $v(m)$ has a linear lower bound.
Symmetric Alcoved Polytopes
Authors: Werner Annette , Yu Josephine 
Published: January 2020

Generalized alcoved polytopes are polytopes whose facet normals are roots in a given root system. We call a set of points in an alcoved polytope a generating set if there does not exist a strictly smaller alcoved polytope containing it. The type $A$ alcoved polytopes are precisely the tropical polytopes that are also convex in the usual sense. In this case the tropical generators form a generating set. We show that for any root system other than $F_4$, every alcoved polytope invariant under the natural Weyl group action has a generating set of cardinality equal to the Coxeter number of the root system.
On the Number of Spanning Trees in Random Regular Graphs
Authors: Greenhill Catherine , Kwan Matthew , Wind David 
Published: January 2020

Let $d\geq 3$ be a fixed integer. We give an asympotic formula for the expected number of spanning trees in a uniformly random $d$-regular graph with $n$ vertices. (The asymptotics are as $n\to\infty$, restricted to even $n$ if $d$ is odd.) We also obtain the asymptotic distribution of the number of spanning trees in a uniformly random cubic graph, and conjecture that the corresponding result holds for arbitrary (fixed) $d$. Numerical evidence is presented which supports our conjecture.
On Graphs Having no Flow Roots in the Interval $(1,2)$
Authors: Dong F.M. 
Published: January 2020

For any graph $G$, let $W(G)$ be the set of vertices in $G$ of degrees larger than 3. We show that for any bridgeless graph $G$, if $W(G)$ is dominated by some component of $G - W(G)$, then $F(G,\lambda)$ has no roots in the interval (1,2), where $F(G,\lambda)$ is the flow polynomial of $G$. This result generalizes the known result that $F(G,\lambda)$ has no roots in (1,2) whenever $|W(G)| \leq 2$. We also give some constructions to generate graphs whose flow polynomials have no roots in $(1,2)$.
Characterization of $(2m,m)$-Paintable Graphs
Authors: Mahoney Thomas , Meng Jixian , Zhu Xuding 
Published: January 2020

In this paper, we prove that for any graph $G$ and any positive integer $m$, $G$ is $(2m,m)$-paintable if and only if $G$ is 2-paintable. It was asked by Zhu in 2009 whether $k$-paintable graphs are $(km,m)$-paintable for any positive integer $m$. Our result answers this question in the affirmative for $k=2$.
From Clutters to Matroids
Authors: Martí-Farré Jaume 
Published: January 2020

This paper deals with the question of completing a monotone increasing family of subsets $\Gamma$ of a finite set $\Omega$ to obtain the dependent sets of a matroid. Specifically, we provide several natural processes for transforming the clutter $\Lambda$ of the inclusion-minimal subsets of the family $\Gamma$ into the set of circuits ${\cal C}({\cal M})$ of a matroid ${\cal M}$ with ground set $\Omega$. In addition, by combining these processes, we prove that all the minimal matroidal completions of the family can be obtained.
A Combinatorial Identity of Multiple Zeta Values with Even Arguments
Authors: Ding Shifeng , Feng Lihua , Liu Weijun 
Published: January 2020

Let $\zeta(s_1,s_2,\cdots,s_k;\alpha)$ be the multiple Hurwitz zeta function. Given two positive integers $k$ and $n$ with $k\leq n$, let $E(2n, k;\alpha)$ be the sum of all multiple zeta values with even arguments whose weight is $2n$ and whose depth is $k$. In this note we present some generating series for the numbers $E(2n,k;\alpha)$.
Minimal Crystallizations of 3-Manifolds
Authors: Basak Biplab , Datta Basudeb 
Published: January 2020

We have introduced the weight of a group which has a presentation with number of relations is at most the number of generators. We have shown that the number of facets of any contracted pseudotriangulation of a connected closed 3-manifold $M$ is at least the weight of the fundamental group of $M$. This lower bound is sharp for the 3-manifolds $\mathbb{RP}^3$, $L(3,1)$, $L(5,2)$, $S^1\times S^1 \times S^1$, $S^2 \times S^1$, twisted product of $S^2$ and $S^1$ and $S^3/Q_8$, where $Q_8$ is the quaternion group. Moreover, there is a unique such facet minimal pseudotriangulation in each of these seven cases. We have also constructed contracted pseudotriangulations of $L(kq-1,q)$ with $4(q+k-1)$ facets for $q \geq 3$, $k \geq 2$ and $L(kq+1,q)$ with $4(q+k)$ facets for $q\geq 4$, $k\geq 1$. By a recent result of Swartz, our pseudotriangulations of $L(kq+1, q)$ are facet minimal when $kq+1$ are even. In 1979, Gagliardi found presentations of the fundamental group of a manifold $M$ in terms of a contracted pseudotriangulation of $M$. Our construction is the converse of this, namely, given a presentation of the fundamental group of a 3-manifold $M$, we construct a contracted pseudotriangulation of $M$. So, our construction of a contracted pseudotriangulation of a 3-manifold $M$ is based on a presentation of the fundamental group of $M$ and it is computer-free.
Equicovering Subgraphs of Graphs and Hypergraphs
Authors: Choi Ilkyoo , Kim Jaehoon , Tebbe Amelia , West Douglas B. 
Published: January 2020

As a variation on the $t$-Equal Union Property ($t$-EUP) introduced by Lindström, we introduce the $t$-Equal Valence Property ($t$-EVP) for hypergraphs: a hypergraph satisfies the $t$-EVP if there are $t$ pairwise edge-disjoint subhypergraphs such that for each vertex $v$, the degree of $v$ in all $t$ subhypergraphs is the same. In the $t$-EUP, the subhypergraphs just have the same sets of vertices with positive degree. For both the $2$-EUP and the $2$-EVP, we characterize the graphs satisfying the property and determine the maximum number of edges in a graph not satisfying it. We also study the maximum number of edges in both $k$-uniform and general hypergraphs not satisfying the $t$-EVP.
Isometric Embeddings of Half-Cube Graphs in Half-Spin Grassmannians
Authors: Pankov Mark 
Published: January 2020

Let $\Pi$ be a polar space of type $\textsf{D}_{n}$. Denote by ${\mathcal G}_{\delta}(\Pi)$, $\delta\in \{+,-\}$ the associated half-spin Grassmannians and write $\Gamma_{\delta}(\Pi)$ for the corresponding half-spin Grassmann graphs. In the case when $n\ge 4$ is even, the apartments of ${\mathcal G}_{\delta}(\Pi)$ will be characterized as the images of isometric embeddings of the half-cube graph $\frac{1}{2}H_n$ in $\Gamma_{\delta}(\Pi)$. As an application, we describe all isometric embeddings of $\Gamma_{\delta}(\Pi)$ in the half-spin Grassmann graphs associated to a polar space of type $\textsf{D}_{n'}$ under the assumption that $n\ge 6$ is even.
Extremal Problems for the $p$-Spectral Radius of Graphs
Authors: Kang Liying , Nikiforov Vladimir 
Published: January 2020

The $p$-spectral radius of a graph $G\ $of order $n$ is defined for any real number $p\geq1$ as$$\lambda^{(p)}(G) =\max\{ 2\sum_{\{i,j\}\in E(G)} x_ix_j:x_1,\ldots,x_n\in\mathbb{R}\text{ and }\vert x_{1}\vert ^{p}+\cdots+\vert x_n\vert^{p}=1\} .$$The most remarkable feature of $\lambda^{(p)}$ is that it seamlessly joins several other graph parameters, e.g., $\lambda^{(1)}$ is the Lagrangian, $\lambda^{(2) }$ is the spectral radius and $\lambda^{(\infty) }/2$ is the number of edges. This paper presents solutions to some extremal problems about $\lambda^{(p)}$, which are common generalizations of corresponding edge and spectral extremal problems.Let $T_{r}\left( n\right) $ be the $r$-partite Turán graph of order $n$. Two of the main results in the paper are:(I) Let $r\geq2$ and $p>1.$ If $G$ is a $K_{r+1}$-free graph of order $n$, then$$\lambda^{(p)}(G) <\lambda^{(p)}(T_{r}(n)),$$ unless $G=T_{r}(n)$.(II) Let $r\geq2$ and $p>1.$ If $G\ $is a graph of order $n,$ with$$\lambda^{(p)}(G)>\lambda^{(p)}( T_{r}(n)) ,$$then $G$ has an edge contained in at least $cn^{r-1}$ cliques of order $r+1$, where $c$ is a positive number depending only on $p$ and $r.$
Schubert Polynomials and $k$-Schur Functions
Authors: Benedetti Carolina , Bergeron Nantel 
Published: January 2020

The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function, which we refer to as Schubert vs. Schur problem, can be understood combinatorially from the multiplication in the space of dual $k$-Schur functions. Using earlier work by the second author, we encode both problems by means of quasisymmetric functions. On the Schubert vs. Schur side, we study the poset given by the Bergeron-Sottile's $r$-Bruhat order, along with certain operators associated to this order. Then, we connect this poset with a graph on dual $k$-Schur functions given by studying the affine grassmannian order of Lam-Lapointe-Morse-Shimozono. Also, we define operators associated to the graph on dual $k$-Schur functions which are analogous to the ones given for the Schubert vs. Schur problem. This is the first step of our more general program of showing combinatorially the positivity of the multiplication of a dual $k$-Schur function by a Schur function.
Maximum 4-Degenerate Subgraph of a Planar Graph
Authors: Lukot'ka Robert , Mazák Ján , Zhu Xuding 
Published: January 2020

A graph $G$ is $k$-degenerate if it can be transformed into an empty graph by subsequent removals of vertices of degree $k$ or less. We prove that every connected planar graph with average degree $d \ge 2$ has a $4$-degenerate induced subgraph containing at least $ (38 - d)/36$ of its vertices. This shows that every planar graph of order $n$ has a $4$-degenerate induced subgraph of order more than $8/9 \cdot n$. We also consider a local variation of this problem and show that in every planar graph with at least 7 vertices, deleting a suitable vertex allows us to subsequently remove at least 6 more vertices of degree four or less.
Mutations of Fake Weighted Projective Spaces
Authors: Coates Tom , Gonshaw Samuel , Kasprzyk Alexander , Nabijou Navid 
Published: January 2020

We characterise mutations between fake weighted projective spaces, and give explicit formulas for how the weights and multiplicity change under mutation. In particular, we prove that multiplicity-preserving mutations between fake weighted projective spaces are mutations over edges of the corresponding simplices. As an application, we analyse the canonical and terminal fake weighted projective spaces of maximal degree.
Wieland Drift for Triangular Fully Packed Loop Configurations
Authors: Beil Sabine , Fischer Ilse , Nadeau Philippe 
Published: January 2020

Triangular fully packed loop configurations (TFPLs) emerged as auxiliary objects in the study of fully packed loop configurations on a square (FPLs) corresponding to link patterns with a large number of nested arches. Wieland gyration, on the other hand, was invented to show the rotational invariance of the numbers $A_\pi$ of FPLs corresponding to a given link pattern $\pi$. The focus of this article is the definition and study of Wieland drift on TFPLs. We show that the repeated application of this operation eventually leads to a configuration that is left invariant. We also provide a characterization of such stable configurations. Finally we apply Wieland drift to the study of TFPL configurations, in particular giving new and simple proofs of several results.
Counting the Palstars
Authors: Richmond L. Bruce , Shallit Jeffrey O 
Published: January 2020

A palstar (after Knuth, Morris, and Pratt) is a concatenation of even-length palindromes. We show that, asymptotically, there are $\Theta(\alpha_k^n)$ palstars of length $2n$ over a $k$-letter alphabet, where $\alpha_k$ is a constant such that $2k-1 < \alpha_k < 2k-{1 \over 2}$. In particular, $\alpha_2\doteq 3.33513193$.
Summation of Rational Series Twisted by Strongly $B$-multiplicative Coefficients
Authors: Allouche Jean-Paul , Sondow Jonathan 
Published: January 2020

We evaluate in closed form series of the type $\sum u(n) R(n)$, with $(u(n))_n$ a strongly $B$-multiplicative sequence and $R(n)$ a (well-chosen) rational function. A typical example is:$$\sum_{n \geq 1} (-1)^{s_2(n)} \frac{4n+1}{2n(2n+1)(2n+2)} = -\frac{1}{4}$$where $s_2(n)$ is the sum of the binary digits of the integer $n$. Furthermore closed formulas for series involving automatic sequences that are not strongly $B$-multiplicative, such as the regular paperfolding and Golay-Shapiro-Rudin sequences, are obtained; for example, for integer $d \geq 0$:$$\sum_{n \geq 0} \frac{v(n)}{(n+1)^{2d+1}} = \frac{\pi^{2d+1} |E_{2d}|}{(2^{2d+2}-2)(2d)!}$$where $(v(n))_n$ is the $\pm 1$ regular paperfolding sequence and $E_{2d}$ is an Euler number.
Power Sum Expansion of Chromatic Quasisymmetric Functions
Authors: Athanasiadis Christos A. 
Published: January 2020

The chromatic quasisymmetric function of a graph was introduced by Shareshian and Wachs as a refinement of Stanley's chromatic symmetric function. An explicit combinatorial formula, conjectured by Shareshian and Wachs, expressing the chromatic quasisymmetric function of the incomparability graph of a natural unit interval order in terms of power sum symmetric functions, is proven. The proof uses a formula of Roichman for the irreducible characters of the symmetric group.
Motzkin Paths, Motzkin Polynomials and Recurrence Relations
Authors: Oste Roy , Van der Jeugt Joris 
Published: January 2020

We consider the Motzkin paths which are simple combinatorial objects appearing in many contexts. They are counted by the Motzkin numbers, related to the well known Catalan numbers. Associated with the Motzkin paths, we introduce the Motzkin polynomial, which is a multi-variable polynomial "counting" all Motzkin paths of a certain type. Motzkin polynomials (also called Jacobi-Rogers polynomials) have been studied before, but here we deduce some properties based on recurrence relations. The recurrence relations proved here also allow an efficient computation of the Motzkin polynomials. Finally, we show that the matrix entries of powers of an arbitrary tridiagonal matrix are essentially given by Motzkin polynomials, a property commonly known but usually stated without proof.
Intersections of Shifted Sets
Authors: Di Nasso Mauro 
Published: January 2020

We consider shifts of a set $A\subseteq\mathbb{N}$ by elements from another set $B\subseteq\mathbb{N}$, and prove intersection properties according to the relative asymptotic size of $A$ and $B$. A consequence of our main theorem is the following: If $A=\{a_n\}$ is such that $a_n=o(n^{k/k-1})$, then the $k$-recurrence set $R_k(A)=\{x\mid |A\cap(A+x)|\ge k\}$ contains the distance sets of arbitrarily large finite sets.
Distributions Defined by $q$-Supernomials, Fusion Products, and Demazure Modules
Authors: Kousidis Stavros , Schulte-Geers Ernst 
Published: January 2020

We prove asymptotic normality of the distributions defined by $q$-supernomials, which implies asymptotic normality of the distributions given by the central string functions and the basic specialization of fusion modules of the current algebra of $\frak{sl}_2$. The limit is taken over linearly scaled fusion powers of a fixed collection of irreducible representations. This includes as special instances all Demazure modules of the affine Kac-Moody algebra associated to $\frak{sl}_2$. Along with an available complementary result on the asymptotic normality of the basic specialization of graded tensors of the type $A$ standard representation, our result is a central limit theorem for a serious class of graded tensors. It therefore serves as an indication towards universal behavior: The central string functions and the basic specialization of fusion and, in particular, Demazure modules behave asymptotically normal, as the number of fusions scale linearly in an asymptotic parameter, $N$ say.
Neutralizing Free Choice Items via Maximal Domain Restriction: Farsi -i Indefinites
Authors: Alonso-Ovalle Luis , Moghiseh Esmail 
Published: January 2020

This paper identifies two types of free choice items (FCIs) in Farsi: yek-i DPs and har -i DPs. Their distribution and interpretation pose a puzzle: yek -i DPs pattern with other existential FCIs, and har -i DPs with other universal FCIs, but both items lose their prototypical FCI behavior when they combine with the accusative marker -ro. The paper shows that the loss of FCI behavior follows from an alternative-based analysis of FCIs (Chierchia 2013) under some assumptions about the semantic effect of -ro. The analysis parallels the explanation for the loss of FCI status of Spanish algunos presented in Alonso-Ovalle & Menéndez-Benito 2011 in that it also relies on the derivation of alternatives that are equivalent to the assertion, hence not excludable.
Penser les rapports familles-institutions, enjeux d’une recherche-action : déconstruire les injonctions paradoxales, instaurer la triangulation
Authors: Montandon Christiane , Schwartz Agnès , Maurin Souvignet Aurélie 
Published: January 2020

Cet article est le fruit des premières analyses et des premiers résultats d’une recherche-action intitulée « Penser les rapports familles-institutions : enjeux de la parentalité contemporaine », et portée par une équipe pluriprofessionnelle, multisite et plurigénérationnelle. Deux volets cliniques de ce travail nous permettent de développer la spécificité de notre démarche de médiation, dans le contexte particulier des liens, des relations et des rapports entre famille et institution en ce qu’ils sont marqués par la confusion et par les injonctions paradoxales.
Familles et institution, entre entente et mésentente
Authors: Eiguer Alberto 
Published: January 2020

Les conflits entre famille et institution de soin peuvent affecter la qualité des prises en charge. Le soignant risque de se sentir désorienté quant à ses objectifs – au sens de sa fonction – et à ses compétences. Pour étudier ces difficultés, l’auteur a recours aux idées de groupe et notamment de groupe analytique « opératoire » selon E. Pichon-Rivière : l’idée de tâche et celle de fantasmes partagés sont explorées ainsi qu’un fantasme spécifique, celui du vol d’enfant. Aussi bien les membres de la famille que les acteurs institutionnels en sont animés, la famille redoutant que ceux-ci se proposent de les « remplacer » auprès de l’enfant ; et ceux-ci imaginant qu’« ils peuvent faire mieux qu’eux ». Sont analysés ensuite les liens entre ce fantasme et ceux de scène primitive et de roman familial. La thérapie familiale psychanalytique ( tfp) permet d’aborder ces difficultés entre famille et institution devenant tampon, régulation et facteur de dépassement. Un cas de tfp illustre ces propos.
La relation à l’objet dans la clinique de la grande précarité : une approche transversale
Authors: Humphreys Derek , Tsoni Evangelia , Pawlik Claude 
Published: January 2020

Cette réflexion sur le statut de l’objet se fait à partir de l’expérience clinique d’une équipe mobile de psychologues travaillant auprès des sujets migrants. Intéressés par les possibilités créatives de cette clinique, nous abordons la complexité du rapport à l’autre dans la grande précarité, lorsque seulement quelques rencontres fortuites semblent possibles. Le symptôme, dans son lien à un désir impossible pour le sujet en grande précarité, nous permet de renverser un désir gelé. Aussi, dans l’attention ici portée aux parcours des sujets errants et aux choses qu’ils portent, nous questionnons les modes habituels d’échange dans la culture. Cette ouverture considère une dimension anthropologique, historique et culturelle des liens entre un sujet et ses « trajets ».
Les Fiancés de Manzoni : radiographie d’un texte en mouvement
Authors: Raboni Giulia 
Published: January 2020

Cette étude présente les étapes de la longue gestation des Fiancés, en prêtant une attention particulière au « Second manuscrit » du roman, édité pour la première fois en 2016 et dont la situation textuelle complexe est mise en évidence : en « amont », ce manuscrit intègre matériellement certains documents de la première rédaction du roman, dont il réutilise de nombreuses pages ; en « aval », il entretient un lien direct avec la révision des feuilles préparées par le copiste pour la censure, avec le début de l’impression et la correction des épreuves. Il s’agit donc d’un texte en mouvement qui implique que l’on en donne une interprétation non pas globale mais mise en regard avec les autres phases rédactionnelles du roman ; malgré cela, la publication intégrale de ce second brouillon, auparavant relégué dans les notes de l’édition princeps du roman, a permis de mieux percevoir la lente et pragmatique transformation des choix linguistiques de Manzoni jusqu’à l’édition de 1827 et de saisir les prémices de la crise du rapport entre vérité et vraisemblable qui ne sera explicitée publiquement que dans les années 1850 avec la parution de l’essai Sur le roman historique, une crise dont les indices significatifs sont la mise à l’écart puis la récriture de l’Histoire de la colonne infâme.