具有固定得分向量的竞赛矩阵的数目

本文考虑以允许平局的单循环比赛为模型的竞赛图（二重完全图）的定向图的邻接矩阵（竞赛矩阵）．给出了具有特殊得分向量的竞赛矩阵的数目,得到了具有ｎ阶强有效得分向量的竞赛矩阵的数目的下确界,并给出了达到此下界的得分向量的刻划．     

强连通竞赛图的圈分解

设T为n阶强连通竞赛图．本文通过详细刻画不能进行圈分解的强连通竞赛图的特征，证明了满足max{^ ，δ^-}≥5k-5和k≥2的强连通竞赛图T,能够分解为k个圈．     

A remark on degree sequences of multigraphs

A sequence {d ₁, d ₂, . . . , d _n } of nonnegative integers is graphic (multigraphic) if there exists a simple graph (multigraph) with vertices v ₁, v ₂, . . . , v _n such that the degree d(v _i ) of the vertex v _i equals d _i for each i = 1, 2, . . . , n. The (multi) graphic degree sequence problem is: Given a sequence of nonnegative integers, determine whether it is (multi)graphic or not. In this paper we characterize sequences that are multigraphic in a similar way, Havel (Časopis Pěst Mat 80:477–480, 1955) and Hakimi (J Soc Indust Appl Math 10:496–506, 1962) characterized graphic sequences. Results of Hakimi (J Soc Indust Appl Math 10:496–506, 1962) and Butler, Boesch and Harary (IEEE Trans Circuits Syst CAS-23(12):778–782, 1976) follow.     

具有四个不同特征值的竞赛矩阵

设A是n阶竞赛矩阵，k是非负整数。文[3]刻划了恰好有三个不同特征值的n阶竞赛矩阵，文[4]刻划了恰好有四个不同特征值并且0作为一个一重特征值的n阶竞赛矩阵。在这篇文章中我们主要研究了两个问题：（1）讨论当k是A的特征值时A的性质。（2）刻划恰好有四个不同特征值并且k作为一个一重特征值的全部n阶竞赛矩阵。     

正则竞赛矩阵的数目和竞赛矩阵的整数特征值

本文给出了ｎ阶正则竞赛矩阵的数目的一个下界，该下界优于文献中的结果；讨论了正竞赛矩阵的性质；得到了整数１为竞赛矩阵的特征值的等价条件及这类矩阵的谱根与得分向量之间的关系．     

Classical Kloosterman sums: Representation theory, magic squares, and Ramanujan multigraphs

We consider a certain finite group for which Kloosterman sums appear as character values. This leads us to consider a concrete family of commuting hermitian matrices which have Kloosterman sums as eigenvalues. These matrices satisfy a number of “magical” combinatorial properties and they encode various arithmetic properties of Kloosterman sums. These matrices can also be regarded as adjacency matrices for multigraphs which display Ramanujan-like behavior.     

Regular multigraphs and their application to the Monte Carlo evaluation of moments of non-linear functions of Gaussian random variables

This paper expands on the multigraph method for expressing moments of non-linear functions of Gaussian random variables. In particular, it includes a list of regular multigraphs that is needed for the computation of some of these moments. The multigraph method is then used to evaluate numerically the moments of non-Gaussian self-similar processes. These self-similar processes are of interest in various applications and the numerical value of their marginal moments yield qualitative information about the behavior of the probability tails of their marginal distributions.     

Extension of Arrow's theorem to symmetric sets of tournaments

Arrow's impossibility theorem [K.J. Arrow, Social Choice and Individual Values, Wiley, New York, NY, 1951] shows that the set of acyclic tournaments is not closed to non-dictatorial Boolean aggregation. In this paper we extend the notion of aggregation to general tournaments and we show that for tournaments with four vertices or more any proper symmetric (closed to vertex permutations) subset cannot be closed to non-dictatorial monotone aggregation and to non-neutral aggregation. We also demonstrate a proper subset of tournaments that is closed to parity aggregation for an arbitrarily large number of vertices. This proves a conjecture of Kalai [Social choice without rationality, Reviewed NAJ Economics 3(4)] for the non-neutral and the non-dictatorial and monotone cases and gives a counter example for the general case.     

Reconstructible and Half-Reconstructible Tournaments: Application to Their Groups of Hemimorphisms

Let T and T¹ be tournaments with n elements, E a basis for T, E′ a basis for T′, and k ≥ 3 an integer. The dual of T is the tournament T” of basis E defined by T(x, y) = T(y, x) for all x, y ε E. A hemimorphism from T onto T′ is an isomorphism from T onto T” or onto T. A k-hemimorphism from T onto T′ is a bijection f from E to E′ such that for any subset X of E of order k the restrictions T/X and T¹/f(X) are hemimorphic. The set of hemimorphisms of T onto itself has group structure, this group is called the group of hemimorphisms of T. In this work, we study the restrictions to n – 2 elements of a tournament with n elements. In particular, we prove: Let k ≥ 3 be an integer, T a tournament with n elements, where n ≥ k + 5. Then the following statements are equivalent: (i) All restrictions of T to subsets with n – 2 elements are k-hemimorphic. (ii) All restrictions of T to subsets with n – 2 elements are 3-hemimorphic. (iii) All restrictions of T to subsets with n – 2 elements are hemimorphic. (iv) All restrictions of T to subsets with n – 2 elements are isomorphic, (v) Either T is a strict total order, or the group of hemimorphisms of T is 2-homogeneous.     

Monochromatic Paths and at Most 2-Coloured Arc Sets in Edge-Coloured Tournaments

We call the tournament T an m-coloured tournament if the arcs of T are coloured with m-colours. If v is a vertex of an m-coloured tournament T, we denote by ξ(v) the set of colours assigned to the arcs with v as an endpoint. In this paper is proved that if T is an m-coloured tournament with |ξ(v)|≤2 for each vertex v of T, and T satisfies at least one of the two following properties (1) m≠3 or (2) m=3 and T contains no C₃ (the directed cycle of length 3 whose arcs are coloured with three distinct colours). Then there is a vertex v of T such that for every other vertex x of T, there is a monochromatic directed path from x to v. Received: April, 2003     

An extension to a theorem of Himmelberg

This paper extends a widely used theorem of Himmelberg to topological vector spaces whose completion have a separating dual.     

A generalisation of a theorem of Koldunov with an elementary proof

We generalize a Theorem of Koldunov [2] and prove that a disjointness proserving quasi-linear operator between Resz spaces has the Hammerstein property.     

Convolution semigroups and central limit theorem associated with a dual convolution structure

We consider hypergroups associated with Jacobi functions ⁽⁾ (x), (–1/2). We prove the existence of a dual convolution structure on [0,+[i(]0,s ₀]{{) =++1,s ₀=min(,–+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem.     

Generalization of a theorem of Luxemburg and Zaanen

We give a generalization of a result of Luxemburg and Zaanen [6] and we deduce some interesting consequences.     

Largest regular multigraphs with three distinct eigenvalues

We deal with connected $k$-regular multigraphs of order $n$ that has only three distinct eigenvalues. In this paper, we study the largest possible number of vertices of such a graph for given $k$. For $k=2,3,7$, the Moore graphs are largest. For $k\ne 2,3,7,57$, we show an upper bound $n\le k^2?k+1$, with equality if and only if there exists a finite projective plane of order $k?1$ that admits a polarity.     

Vertex-disjoint directed cycles of prescribed length in tournaments with given minimum out-degree and in-degree

In a recent paper, Bessy, Sereni and the author (see [3]) have proved that for r≥1, a tournament with minimum out-degree and in-degree both greater than or equal to 2r−1 contains at least r vertex-disjoint directed triangles. In this paper, we generalize this result; more precisely, we prove that for given integers q≥3 and r≥1, a tournament with minimum out-degree and in-degree both greater than or equal to (q−1)r−1 contains at least r vertex-disjoint directed cycles of length q. We will use an auxiliary result established in [3], concerning a union of sets contained in another union of sets. We finish by giving a lower bound on the maximum number of vertex-disjoint directed cycles of length q when only the minimum out-degree is supposed to be greater than or equal to (q−1)r−1.     

A restriction theorem associated with the generalized Sublaplacian

In this paper, we investigate the generalized Sublaplacian. We give the expression of the restriction operators explicitly. By introducing the generalized -twisted convolutions, we obtain the estimates of the restriction operators in the mixedL ^p spaces. Finally, we get a restriction theorem associated with the generalized Sublaplacian.     

Cycle decompositions of complete multigraphs

It is shown that the obvious necessary conditions for the existence of a decomposition of the complete multigraph with n vertices and with λ edges joining each pair of distinct vertices into m‐cycles, or into m‐cycles and a perfect matching, are also sufficient. This result follows as an easy consequence of more general results which are obtained on decompositions of complete multigraphs into cycles of varying lengths. © 2010 Wiley Periodicals, Inc. J Combin Designs 19:42‐69, 2010     

Identities for non-crossing graphs and multigraphs

We refine an identity between the numbers of certain non-crossing graphs and multigraphs, by modifying a bijection found by P. Podbrdský [A bijective proof of an identity for noncrossing graphs, Discrete Math. 260 (2003) 249-253]. We also prove a new identity between the number of acyclic non-crossing graphs with n vertices and k edges (isolated vertices allowed and no multiple edges allowed), and the number of non-crossing connected graphs with n edges and k vertices (multiple edges allowed and no isolated vertices allowed).