bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the decomposition of λK into regular tournaments of order 5
Authors: Mahmoodi A. , Mathon R. 
Published: June 2007

AbstractAn RTD[5,λ; v] is a decomposition of the complete symmetric directed multigraph, denoted by λK, into regular tournaments of order 5. In this article we show that an RTD[5,λ; v] exists if and only if (v−1)λ ≡ 0 (mod 2) and v(v−1)λ ≡ 0 (mod 10), except for the impossible case (v,λ) = (15,1). Furthermore, we show that for each v ≡ 1,5 (mod 20), v ≠ 5, there exists a B[5,2; v] which is not RT5‐directable. © 1994 John Wiley & Sons, Inc.
The preparata codes and a class of 4‐designs
Authors: Baartmans Alphonse H. , Bluskov Iliya , Tonchev Vladimir D. 
Published: June 2007

AbstractAn extension theorem for t‐designs is proved. As an application, a class of 4‐(4m + 1,5,2) designs is constructed by extending designs related to the 3‐designs formed by the minimum weight vectors in the Preparata code of length n = 4m, m ≥ 2. © 1994 John Wiley & Sons, Inc.
Incomplete perfect mendelsohn designs with block size 4 and holes of size 2 and 3
Authors: Bennett F. E. , Shen H. , Yin J. 
Published: June 2007

AbstractLet v, k, and n be positive integers. An incomplete perfect Mendelsohn design, denoted by k‐IPMD(v, n), is a triple (X, Y, 𝔹) where X is a v‐set (of points), Y is an n‐subset of X, and 𝔹 is a collection of cyclically ordered k‐subsets of X (called blocks) such that every ordered pair (a, b) ∈ (X × X)\(Y × Y) appears t‐apart in exactly one block of 𝔹 and no ordered pair (a,b) ∈ Y × Y appears in any block of 𝔹 for any t, where 1 ≤ t ≤ k − 1. In this article, the necessary conditions for the existence of a 4‐IPMD(v, n), namely (v − n) (v − 3n − 1) ≡ 0 (mod 4) and v ≥ 3n + 1, are shown to be sufficient for the case n = 3. For the case n = 2, these conditions are sufficient except for v = 7 and with the possible exception of v = 14,15,18,19,22,23,26,27,30. The latter result provides a useful application to the problem relating to the packing of perfect Mendelsohn designs with block size 4. © 1994 John Wiley & Sons, Inc.
Sharply transitive 1‐factorizations of the complete graph with an invariant 1‐factor
Authors: Korchmáros Gábor 
Published: June 2007

AbstractWe give some simple characterizations of those n for which Kn has a sharply transitive 1‐factorization with an assigned automorphism group that acts sharply transitively on the vertex set and also fixes a 1‐factor. © 1994 John Wiley & Sons, Inc.
There are 526,915,620 nonisomorphic one‐factorizations of K12
Authors: Dinitz Jeffrey H. , Garnick David K. , McKay Brendan D. 
Published: June 2007

AbstractWe enumerate the nonisomorphic and the distinct one‐factorizations of K12. We also describe the algorithm used to obtain the result, and the methods we used to verify these numbers. © 1994 John Wiley & Sons, Inc.
5‐chromatic steiner triple systems
Authors: Fugère Jean , Haddad Lucien , Wehlau David 
Published: June 2007

AbstractWe show that, up to an automorphism, there is a unique independent set in PG(5,2) that meets every hyperplane in 4 points or more. Using this result, we show that PG(5,2) is a 5‐chromatic STS. Moreover, we construct a 5‐chromatic STS(v) for every admissible v ≥ 127. © 1994 John Wiley & Sons, Inc.
Hadamard matrices constructed from supplementary difference sets in the class ℋ︁1
Authors: Xia Ming‐Yuan , Xia Tian‐Bing 
Published: June 2007

AbstractIn this article we give the definition of the class ℋ︁1 and prove: (1) ℋ︁1(v) ≠ ϕ for v ∈ 𝒩 = 𝒩1 ∪ 𝒩2 ∪ 𝒩3 where

(2) there exists 2 − {2q2; q2 ± q, q2;q2 ± q} supplementary difference sets for q2 ∈ 𝒩; (3) there exists an Hadamard matrix of order 4v for v ∈ 𝒩; (4) if t is an order of T‐matrices, there exists an Hadamard matrix of order 4tv for v ∈ 𝒩. © 1994 John Wiley & Sons, Inc.
The spectrum for large sets of disjoint mendelsohn triple systems with any index
Authors: Kang Qing‐De , Lei Jian‐Guo , Chang Yan‐Xun 
Published: June 2007

AbstractThe spectrum for LMTS(v,1) has been obtained by Kang and Lei (Bulletin of the ICA, 1993). In this article, firstly, we give the spectrum for LMTS(v,3). Furthermore, by the existence of LMTS(v,1) and LMTS(v,3), the spectrum for LMTS(v,λ) is completed, that is v ≡ 2 (mod λ), v ≥ λ + 2, if λ ≢ 0(mod 3) then v ≢ 2 (mod 3) and if λ = 1 then v ≠ 6. © 1994 John Wiley & Sons, Inc.
The spectrum of self‐converse DTS
Authors: Kang Qingde , Chang Yanxun , Yang Guihua 
Published: June 2007

AbstractA directed triple system, DTS(v) = (X,ℬ︁), is called self‐converse if it and its converse (X,ℬ︁−1) are isomorphic, where ℬ︁ = {(z,y,x);(x,y,z) ∈ ℬ︁}. In this article, the existence spectrum of self‐converse DTS(v) is given, which is v ≡ 0 or 1 (mod 3) and v ≠ 6. © 1994 John Wiley & Sons, Inc.
The existence of doubly near resolvable (v,3,2)‐BIBDs
Authors: Lamken E. R. 
Published: June 2007

AbstractThe existence of doubly near resolvable (v,2,1)‐BIBDs was established by Mullin and Wallis in 1975. In this article, we determine the spectrum of a second class of doubly near resolvable balanced incomplete block designs. We prove the existence of DNR(v,3,2)‐BIBDs for v ≡ 1 (mod 3), v ≥ 10 and v ∉ {34,70,85,88,115,124,133,142}. The main construction is a frame construction, and similar constructions can be used to prove the existence of doubly resolvable (v,3,2)‐BIBDs and a class of Kirkman squares with block size 3, KS3(v,2,4). © 1994 John Wiley & Sons, Inc.
Embeddings of pure mendelsohn triple systems and pure directed triple systems
Authors: Hao Shen 
Published: June 2007

AbstractIt is proved in this article that the necessary and sufficient conditions for the embedding of a λ‐fold pure Mendelsohn triple system of order v in λ‐fold pure Mendelsohn triple of order u are λu(u − 1) ≡ 0 (mod 3) and u ⩾ 2v + 1. Similar results for the embeddings of pure directed triple systems are also obtained. © 1995 John Wiley & Sons, Inc.
On a class of small 2‐designs over gf(q)
Authors: Miyakawa Masashi , Munemasa Akihiro , Yoshiara Satoshi 
Published: June 2007

AbstractA 2 − (v,k,λ;q) design is a pair (V, B) of a v‐dimensional vector space V over GF(q) and a collection B of k‐dimensional subspaces of V such that each 2‐dimensional subspace of V is contained in exactly λ members of B. Assuming transitivity of their automorphism groups on the nonzero vectors of V, we give a classification of nontrivial such designs for v = 7, q = 2,3 with small λ, together with the nonexistence proof of those designs for v ⩽ 6. © 1995 John Wiley & Sons, Inc.
More cyclic triplewhist tournaments
Authors: Anderson I. , Finizio N. J. 
Published: June 2007

AbstractWe extend the set of values of n for which it is known that a Z‐cyclic triple whist tournament for 4n players exists by proving that if there exists such a tournament for q + 1 players, where q ≡ 3 (mod 4) is prime, then there exists such a tournament for qpa11…pann + 1 players, whenever the pi are primes ≡ 5 (mod 8). © 1995 John Wiley & Sons, Inc.
Zero‐sum block designs and graph labelings
Authors: Tuza Zsolt 
Published: June 2007

AbstractProving a conjecture of Aigner and Triesch, we show that every graph G = (V,E) without isolated vertices and isolated edges admits an edge labeling ξ: E → {0,1}m with binary vectors of length m = [log2 n] + 1 such that the sums.CALLING STATEMENT : (taken modulo 2 componentwise) are mutually distinct, provided that n is sufficiently large. The proof combines probabilistic arguments with explicitly constructed Steiner systems. © 1995 John Wiley & Sons, Inc.
A representation theorem and Z‐cyclic whist tournaments
Authors: Finizio Norman J. 
Published: June 2007

AbstractLet E denote the group of units (i.e., the reduce set of residues) in the ring Z. Here we consider q,p to be primes, q ≡ 3 (mod 4), q ⩾ 7, p ≡ 1 (mod 4). Let W denote a common primitive root of 3, q, and p2. If H denotes the (normal) subgroup of E that is generated by {−1, W}, we show that the factor group E/H is cyclic by demonstrating the existence of an element x in E such that the coset xH has order equal to |E/H|. This order is given by gcd(pn−1(p − 1),q − 1). This representation of E/H is exploited via an appropriate construction to produce Z‐cyclic whist tournaments for 3qpn players. Consequently these results extend those of an early study of Wh(3qpn) that was restricted to gcd(pn−1(p − 1),q − 1) = 2. © 1995 John Wiley & Sons, Inc.
Large sets of 3‐designs from psl(2, q), with block sizes 4 and 5
Authors: Cusack C. A. , Graham S. W. , Kreher D. L. 
Published: June 2007

AbstractWe determine the distribution of 3−(q + 1,k,λ) designs, with k ϵ {4,5}, among the orbits of k‐element subsets under the action of PSL(2,q), for q ϵ 3 (mod 4), on the projective line. As a consequence, we give necessary and sufficient conditions for the existence of a uniformly‐PSL(2,q) large set of 3−(q + 1,k,λ) designs, with k ϵ {4,5} and q ≡ 3 (mod 4). © 1995 John Wiley & Sons, Inc.
On simple radical difference families
Authors: Buratti Marco 
Published: June 2007

AbstractFor q a prime power and k odd (even), we define a (q,k,1) difference family to be radical if each base block is a coset of the kth roots of unity in the multiplicative group of GF(q) (the union of a coset of the (k − 1)th roots of unity in the multiplicative group of GF(q) with zero). Such a family will be denoted by RDF. The main result on this subject is a theorem dated 1972 by R.M. Wilson; it is a sufficient condition for the existence of a (q,k, 1)‐RDF for any k. We improve this result by replacing Wilson's condition with another sufficient but weaker condition, which is proved to be necessary at least for k ⩽ 7. As a consequence, we get new difference families and hence new Steiner 2‐designs. © 1995 John Wiley & Sons, Inc.
A unique arithmetic labeling of hexagonal lattices
Authors: Chang Gerard J. , Hwang F. K. , Wright P. E. , Griggs J. R. 
Published: June 2007

AbstractConsider an r‐layer hexagon consisting of 3r2 + 3r + 1 hexagonal cells. Can one label the cells by the set Nr = {0,1,…, 3r2 + 3r} such that each line of adjacent cells are labeled by numbers forming an arithmetic progression modulo (3r2 + 3r + 1) (in proper ordering)? We show that for each r there exists such a labeling unique up to equivalence. We also study some other related issues. © 1995 John Wiley & Sons, Inc.
Bounds on orthogonal arrays and resilient functions
Authors: Bierbrauer Jürgen 
Published: June 2007

AbstractThe only known general bounds on the parameters of orthogonal arrays are those given by Rao in 1947 [J. Roy. Statist. Soc. 9 (1947), 128–139] for general OAγ(t,k,v) and by Bush [Ann. Math. Stat. 23, (1952), 426–434] [3] in 1952 for the special case γ = 1. We present an algebraic method based on characters of homocyclic groups which yields the Rao bounds, the Bush bound in case t ⩾ v, and more importantly a new explicit bound which for large values of t (the strength of the array) is much better than the Rao bound. In the case of binary orthogonal arrays where all rows are distinct this bound was previously proved by Friedman [Proc. 33rd IEEE Symp. on Foundations of Comput. Sci., (1992), 314–319] in a different setting. We also note an application to resilient functions. © 1995 John Wiley & Sons, inc.
Virtually balanced incomplete block designs for v = 22, k = 8, and λ = 4
Authors: Hedayat A. S. , Stufken J. , Zhang W. G. 
Published: June 2007

AbstractWhen basic necessary conditions for the existence of a balanced incomplete block design are satisfied, the design may still not exist or it may not be known whether it exists. In either case, other designs may be considered for the same parameters. In this article we introduce a class of alternative designs, which we will call virtually balanced incomplete block designs. From a statistical point of view these designs provide efficient alternatives to balanced incomplete block designs, and from a combinatorial point of view they offer challenging new questions. © 1995 John Wiley & Sons, Inc.
On orthogonal double covers of kn and a conjecture of chung and west
Authors: Gronau H.‐D. O. F. , Mullin R. C. , Schellenberg P. J. 
Published: June 2007

AbstractA collection 𝔾 = {G1, G2,…,Gn} of spanning subgraphs of Kn is called an orthogonal double cover if (i) every edge of Kn belongs to exactly two of the Gi's and (ii) any two distinct Gi's intersect in exactly one edge. Chung and West conjectured that there exists an orthogonal double cover of Kn, for all n, in which each Gi has maximum degree 2, and proved this result for n in six of the residue classes modulo 12. In another context, Ganter and Gronau showed that for n ≡ 1 mod 3, n ≠ 10, there exists an orthogonal double cover of Kn in which each Gi consists of an isolated vertex and the vertex disjoint union of K3's (actually these orthogonal double covers result from the solution of the directed version of the problem, which reduces to the undirected case when the orientation of the arcs is ignored). Clearly the covers of Ganter and Gronau satisfy the Chung‐West requirement. In this article, the configurations of Ganter and Gronau are generalized to include the cases n ≡ 0,2 mod 3, and the results are used to provide a unified solution of the Chung‐West problem. For n ≠ 5 mod 6, all the spanning subgraphs in the collection 𝔾 are isomorphic to each other; however, this is not the case when n ≡ 5 mod 6. In addition to solving the Chung‐West problem, we also go on to show that for n ≡ 2 mod 3 and n > 287, there exists an orthogonal double cover of Kn in which each spanning subgraph Gi consists of the vertex‐disjoint union of an isolated vertex, and quadrilateral, and (n−5)/3 triangles. Of the 96 cases with 2 ⩽ n ⩽ 287, 65 cases are resolved and 31 remain open. © 1995 John Wiley & Sons, Inc.
Some simple and automorphism‐free 2‐(15,5,4) designs
Authors: Nowzari‐Dalini A. , Torabi R. , Khosrovshahi G. B. 
Published: June 2007

AbstractA variation of “trading signed design” algorithm is utilized to produce some 104 simple and aotomorphism‐free 2‐(15,5,4) designs. © 1995 John Wiley & Sons, Inc.
Note on large sets of infinite steiner systems
Authors: Cameron Peter J. 
Published: June 2007

AbstractLarge sets of Steiner systems S(t,k,n) exist for all finite t and k with t < k and all infinite n. The vector space analogues exist over a field F for all finite t and k with t < k provided that either v or F is infinite, and n ⩾ 2k − t + 1. This inequality is best possible. © 1995 John Wiley & Sons, Inc.
On r*‐sequenceability and symmetric harmoniousness of groups. II
Authors: Wang Cheng‐De , Leonard Philip A. 
Published: June 2007

AbstractIn this paper we investigate symmetric harmoniousness of groups and connections of this concept to the R*‐sequenceability of groups. We prove that, under suitable assumptions, the direct product of a symmetric harmonious group with a group that is R*‐sequenceable is R*‐sequenceable; we discuss the symmetric harmoniousness of abelian and of nilpotent groups; we also prove that, for a fixed odd prime p, all but possibly finitely many of the nonabelian groups of order pq (q prime, q ≡ 1 (mod p)) are symmetric harmonious. © 1995 John Wiley & Sons, Inc.
Completions of Convexly Ordered Valuation Rings
Authors: Mathews Larry 
Published: June 2007

AbstractWe prove that every convexly ordered valuation ring has a unique completion as a uniform space, which furthermore is a convexly ordered valuation ring. In addition, we give a model theoretic characterisation of complete convexly ordered valuation rings, and give a necessary and sufficient condition for the completion of a convexly ordered valuation ring to be a real closed ring.Mathematics Subject Classification: 03C60, 13L05, 54E15.
The Prime Spectrum of an MV‐Algebra
Authors: Belluce L. P. , Nola Antonio Di , Sessa Salvatore 
Published: June 2007

AbstractIn this paper we show that the prime ideal space of an MV‐algebra is the disjoint union of prime ideal spaces of suitable local MV‐algebras. Some special classes of algebras are defined and their spaces are investigated. The space of minimal prime ideals is studied as well.Mathematics Subject Classification: 03B50, 06D99.
Cofinal Indiscernibles and some Applications to New Foundations
Authors: Körner Friederike 
Published: June 2007

AbstractWe prove a theorem about models with indiscernibles that are cofinal in a given linear order. We apply this theorem to obtain new independence results for Quine's set theory New Foundations, thus solving two open problems in this field.Mathematics Subject Classification: 03C55, 03B15, 03B60, 03E70.
An Extension Principle for Fuzzy Logics
Authors: Gerla Giangiacomo 
Published: June 2007

AbstractLet S be a set, P(S) the class of all subsets of S and F(S) the class of all fuzzy subsets of S. In this paper an “extension principle” for closure operators and, in particular, for deduction systems is proposed and examined. Namely we propose a way to extend any closure operator J defined in P(S) into a fuzzy closure operator J* defined in F(S). This enables us to give the notion of canonical extension of a deduction system and to give interesting examples of fuzzy logics. In particular, the canonical extension of the classical propositional calculus is defined and it is showed its connection with possibility and necessity measures. Also, the canonical extension of first order logic enables us to extend some basic notions of programming logic, namely to define the fuzzy Herbrand models of a fuzzy program. Finally, we show that the extension principle enables us to obtain fuzzy logics related to fuzzy subalgebra theory and graded consequence relation theory.Mathematics Subject Classification: 03B52.
Reflection of Long Game Formulas
Authors: Heikkilä Heikki , Väänänen Jouko 
Published: June 2007

AbstractWe study game formulas the truth of which is determined by a semantical game of uncountable length. The main theme is the study of principles stating reflection of these formulas in various admissible sets. This investigation leads to two weak forms of strict‐II11 reflection (or ∑1‐compactness). We show that admissible sets such as H(ω2) and Lω2 which fail to have strict‐II11 reflection, may or may not, depending on set‐theoretic hypotheses satisfy one or both of these weaker forms.Mathematics Subject Classification: 03C70, 03C75.
On Solvable Congruences in Finitely Decidable Varieties
Authors: Valeriote Matthew A. 
Published: June 2007

AbstractIn this paper we establish the (1, 2)‐ and (2, 1)‐transfer principles for finitely decidable locally finite varieties, where a class of structures is finitely decidable if the first order theory of its finite members is recursive. The transfer principles deal with the local structure of finite algebras and have strong global consequences.Mathematics Subject Classification: 08A05, 03C13, 08B05, 08B10.
Omega‐ and Beta‐Models of Alternative Set Theory
Authors: Tzouvaras Athanassios 
Published: June 2007

AbstractWe present the axioms of Alternative Set Theory (AST) in the language of second‐order arithmetic and study its ω‐ and β‐models. These are expansions of the form (M, M), M ⊆ P(M), of nonstandard models M of Peano arithmetic (PA) such that (M, M) ⊩ AST and ω ϵ M. Our main results are: (1) A countable M ⊩ PA is β‐expandable iff there is a regular well‐ordering for M. (2) Every countable β‐model can be elementarily extended to an ω‐model which is not a β‐model. (3) The Ω‐orderings of an ω‐model (M, M) are absolute well‐orderings iff the standard system SS(M) of M is a β‐model of A−2. (4) There are ω‐expandable models M such that no ω‐expansion of M contains absolute Ω‐orderings. (5) There are s‐expandable models (i. e., their ω‐expansions contain only absolute Ω‐orderings) which are not β‐expandable. (6) For every countable β‐expansion M of M, there is a generic extension M[G] which is also a β‐expansion of M. (7) If M is countable and β‐expandable, then there are regular orderings <1, <2 such that neither <1 belongs to the ramified analytical hierarchy of the structure (M, <2), nor <2 to that of (M, <1). (8) The result (1) can be improved as follows: A countable M ⊩ PA is β‐expandable iff there is a semi‐regular well‐ordering for M.
Existentially Complete Nerode Semirings
Authors: McLaughlin Thomas G. 
Published: June 2007

AbstractLet Λ denote the semiring of isols. We characterize existential completeness for Nerode subsemirings of Λ, by means of a purely isol‐theoretic “Σ1 separation property”. (A “concrete” characterization that is not Λ‐theoretic is well known: the existentially complete Nerode semirings are the ones that are isomorphic to Σ1 ultrapowers.) Our characterization is purely isol‐theoretic in that it is formulated entirely in terms of the extensions to Λ of the Σ1 subsets of the natural numbers. Advantage is taken of a special kind of isol first conjectured to exist by Ellentuck and first proven to exist by Barback (unpublished). In addition, we strengthen the negative part of [13] by showing that existential completeness is not secured, for a given Nerode semiring, by either (i) a certain “functional closure” property for the extensions of partial recursive functions or (ii) the property of “pulling in” some portion of each partial recursive fiber; these latter results are perhaps a little surprising.
Invariant Constructions of Simple and Maximal Sets
Authors: Weber Frank P. 
Published: June 2007

AbstractThe main results of the present paper are the following theorems: 1. There is no e ∈ ω such that for any A, B ⊆ ω, SA = W is simple in A, and if A′ T B′, then SA =* SB. 2 There is an e ∈ ω such that for any A, B ⊆ ω, MA = We is incomplete maximal in A, and if A =* B, then MA T MB.
Polynomial Time Uniform Word Problems
Authors: Burris Stanley 
Published: June 2007

AbstractWe have two polynomial time results for the uniform word problem for a quasivarietyQ: (a) The uniform word problem forQcan be solved in polynomial time iff one can find a certain congruence on finite partial algebras in polynomial time. (b) LetQ* be the relational class determined byQ. If any universal Horn class between the universal closureS(Q*) and the weak embedding closureS̄(Q*) ofQ* is finitely axiomatizable then the uniform word problem forQis solvable in polynomial time. This covers Skolem's 1920 solution to the uniform word problem for lattices and Evans' 1953 applications of the weak embeddability property for finite partialValgebras.
Local Density of Kleene Degrees
Authors: Muraki Hisato 
Published: June 2007

AbstractConcerning Post's problem for Kleene degrees and its relativization, Hrbacek showed in [1] and [2] that if V = L, then Kleene degrees of coanalytic sets are dense, and then for all K ⊆ωω, there are N1 sets which are Kleene semirecursive in K and not Kleene recursive in each other and K. But the density of Kleene semirecursive in K Kleene degrees is not obtained from these theorems. In this note, we extend these theorems by showing that if V = L, then for all K ⊆ ωω, Kleene semirecursive in K Kleene degrees are dense above K.
On Commutative and Nonassociative Syntactic Calculi and Categorial Grammars
Authors: Kandulski Maciej 
Published: June 2007

AbstractTwo axiomatizations of the nonassociative and commutative Lambek syntactic calculus are given and their equivalence is proved. The first axiomatization employs Permutation as the only structural rule, the second one, with no Permutation rule, employs only unidirectional types. It is also shown that in the case of the Ajdukiewicz calculus an analogous equivalence is valid only in the case of a restricted set of formulas. Unidirectional axiomatizations are employed in order to establish the generative power of categorial grammars based on the nonassociative and commutative Lambek calculus with product. Those grammars produce CF‐languages of finite degree generated by CF‐grammars closed with respect to permutations.