相关论文: A Theory of Tournament Representations

In the problem {\sc Min-DESC}, we are given a digraph $D$ and an integer $k$, and asked if there exists a set $A'$ of at most $k$ arcs in $D$, such that if we remove the arcs of $A'$, in the resulting digraph every strong component is…

Given a tournament $T$, the problem MaxCT consists of finding a maximum (arc-disjoint) cycle packing of $T$. In the same way, MaxTT corresponds to the specific case where the collection of cycles are triangles (i.e. directed 3-cycles).…

The paper suggests a family of paired comparison-based scoring procedures for ranking the participants of a Swiss system chess team tournament. We present the challenges of ranking in Swiss system, the features of individual and team…

We develop a unified representation theory for the categories of finite subsets and relation-preserving maps of highly homogeneous relational structures classified by Cameron. For any commutative coefficient ring $k$, we extend the…

The classical paradox of social choice theory asserts that there is no fair way to deterministically select a winner in an election among more than two candidates; the only definite collective preferences are between individual pairs of…

Estimating the linear dimensionality of a data set in the presence of noise is a common problem. However, data may also be corrupted by monotone nonlinear distortion that preserves the ordering of matrix entries but causes linear methods…

It is well known that a tournament (complete oriented graph) on $n$ vertices has at most ${1/4}\binom{n}{3}$ directed triangles, and that the constant 1/4 is best possible. Motivated by some geometric considerations, our aim in this paper…

A $k$-tournament $H$ on $n$ vertices is a pair $(V, A)$ for $2\leq k\leq n$, where $V(H)$ is a set of vertices, and $A(H)$ is a set of all possible $k$-tuples of vertices, such that for any $k$-subset $S$ of $V$, $A(H)$ contains exactly one…

Word-representable graphs, characterized by the existence of a semi-transitive orientation, form a well-studied class of graphs. Comparability graphs form another well-studied class and constitute a subclass of word-representable graphs.…

Gishboliner, Krivelevich, and Michaeli (2023) conjectured the following generalization of Dirac's theorem: If the minimum degree $\delta$ of an $n$-vertex oriented graph $G$ is greater or equal to $n/2$, then $G$ has a Hamilton oriented…

For any truncated path algebra $\Lambda$ of a quiver, we classify, by way of representation-theoretic invariants, the irreducible components of the parametrizing varieties $\mathbf{Rep}_{\mathbf{d}}(\Lambda)$ of the $\Lambda$-modules with…

A tournament $T$ is a tournament completion of a bipartite tournament $D$ if $D$ is a spanning subdigraph of $T$, i.e., $V(D)=V(T)$ and $A(D)\subseteq A(T)$. If $C$ is a $k$-dicycle (i.e., directed cycle of length $k$) in a tournament…

A tournament is called locally transitive if the outneighbourhood and the inneighbourhood of every vertex are transitive. Equivalently, a tournament is locally transitive if it avoids the tournaments $W_4$ and $L_4$, which are the only…

Auslander-Reiten theory is fundamental to study categories which appear in representation theory, for example, modules over artin algebras, Cohen-Macaulay modules over Cohen-Macaulay rings, lattices over orders, and coherent sheaves on…

In a generalized tournament, players may have an arbitrary number of matches against each other and the outcome of the games is measured on a cardinal scale with a lower and upper bound. An axiomatic approach is applied to the problem of…

The permanent vs. determinant problem is one of the most important problems in theoretical computer science, and is the main target of geometric complexity theory proposed by Mulmuley and Sohoni. The current best lower bound for the…

In 2000 Allen Schwenk, using a well-known mathematical model of matchplay tournaments in which the probability of one player beating another in a single match is fixed for each pair of players, showed that the classical single-elimination,…

Let $X=X(n,q)$ be the set of $n\times n$ Hermitian matrices over $\mathbb{F}_{q^2}$. It is well known that $X$ gives rise to a metric translation association scheme whose classes are induced by the rank metric. We study $d$-codes in this…

Using a switching operation on tournaments we obtain some new lower bounds on the Tur\'{a}n number of the $r$-graph on $r+1$ vertices with $3$ edges. For $r=4$, extremal examples were constructed using Paley tournaments in previous work. We…

We develop an abstract axiomatic theory of tie-breaking. A tie-breaking input consists of a finite set N of players, a weak order on N representing the standings to be refined, and an auxiliary information item drawn from a set on which the…