相关论文: Alternating sign matrices and tournaments
We define a tournament to be alternation acyclic if it does not contain a cycle in which descents and ascents alternate. Using a result by Athanasiadis on hyperplane arrangements, we show that these tournaments are counted by the median…
We study Maker/Breaker games on the edges of the complete graph, as introduced by Chvatal and Erdos. We show that in the (m:b) clique game played on K_{N}, the complete graph on N vertices, Maker can achieve a K_{q} for q = (m/(log_{2}(b +…
The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. There are several contexts in which studying the patterns of orthogonal matrices can be useful. One necessary condition for a matrix to be…
Besides the need for a better understanding of networks, there is a need for prescriptive models and tools to specify requirements concerning networks and their associated graph representations. We propose class-based graphs as a means to…
A directed graph $R^{\circ}$ on a set $X$ is a set of ordered pairs of distinct points called \emph{arcs}. It is a tournament when every pair of distinct points is connected by an arc in one direction or the other (and not both). We can…
In this paper, we completely characterize the $m$-step competition graph of a bipartite tournament for any integer $m \ge 2$. In addition, we compute the competition index and the competition period of a bipartite tournament.
Chess championships are often organised as a Swiss-system tournament, causing great challenges in ranking the participants due to the different strength of schedules and possible circular triads. The paper suggests that pairwise comparison…
We start with a bijective proof of Schur's theorem due to Alladi and Gordon and describe how a particular iteration of it leads to some very general theorems on colored partitions. These theorems imply a number of important results,…
We introduce the notions of $\tau$-exceptional and signed $\tau$-exceptional sequences for any finite dimensional algebra. We prove that for a fixed algebra of rank $n$, and for any positive integer $t \leq n$, there is a bijection between…
We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition…
We introduce a method that produces a bijection between the posets ${\rm silt-}{A}$ and ${\rm silt-}{B}$ formed by the isomorphism classes of basic silting complexes over finite-dimensional $k$-algebras $A$ and $B$, by lifting $A$ and $B$…
In this thesis we consider ordered graphs (that is, graphs with a fixed linear ordering on their vertices). We summarize and further investigations on the number of edges an ordered graph may have while avoiding a fixed forbidden ordered…
We establish a bijective correspondence between Smirnov words with balanced letter multiplicities and Hamiltonian paths in complete $m$-partite graphs $K_{n,n,\ldots,n}$. This bijection allows us to derive closed inclusion-exclusion…
We define and study odd analogues of classical geometric and combinatorial objects associated to permutations, namely odd Schubert varieties, odd diagrams, and odd inversion sets. We show that there is a bijection between odd inversion sets…
Inspired by the theory of poset games, we introduce a new compound of impartial combinatorial games and provide a complete analysis in the spirit of the Sprague-Grundy theory. Furthermore, we establish several substitution and reduction…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
In this paper we build a bijection between the meet-irreducible elements of the lattice of the compositions of $n$ with parts in $[1,p]$ equipped with the dominance order, and the edges of the $(n,p)$-Tur\'an graph. Using this bijection, we…
We introduce the notion of balanced strong shift equivalence between square nonnegative integer matrices, and show that two finite graphs with no sinks are one-sided eventually conjugate if and only if their adjacency matrices are conjugate…
We only consider finite structures. With every totally ordered set $V$ and a subset $P$ of $\binom{V}{2}$, we associate the underlying tournament ${\rm Inv}(\underline{V}, P)$ obtained from the transitive tournament $\underline{V}:=(V,…
A signed graph has edge signs. A gain graph has oriented edge gains drawn from a group. We define the combination of the two for the abelian case, in which each oriented edge of a signed graph has a gain from an abelian group, concentrating…