Related papers: Alternating sign matrices and tournaments

We form a "map of tournaments" by adapting the map framework from the world of elections. By a tournament we mean a complete directed graph where the nodes are the players and an edge points from a winner of a game to the loser (with no…

Nearly-doubly-regular tournaments have played significant roles in extremal graph theory. In this note, we construct new cyclotomic nearly-doubly-regular tournaments and determine their spectrum by establishing a new connection between…

Alternating sign matrices with a U-turn boundary (UASMs) are a recent generalization of ordinary alternating sign matrices. Here we show that variations of these matrices are in bijective correspondence with certain symplectic shifted…

In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…

For a fixed finite set of finite tournaments ${\mathcal F}$, the ${\mathcal F}$-free orientation problem asks whether a given finite undirected graph $G$ has an $\mathcal F$-free orientation, i.e., whether the edges of $G$ can be oriented…

We initiate a general study of what we call orientation completion problems. For a fixed class C of oriented graphs, the orientation completion problem asks whether a given partially oriented graph P can be completed to an oriented graph in…

We present a simple bijection between permutation matrices and descending plane partitions without special parts. This bijection is already mentioned in work of P. Lalonde (without giving the details); it involves the inversion words of…

Valuated term orders are studied for the purposes of Gr\"{o}bner theory over fields with valuation. The points of a usual tropical variety correspond to certain valuated terms preorders. Generalizing both of these, the set of all…

If $G$ is a bipartite graph, Hall's theorem \cite{H35} gives a condition for the existence of a matching of $G$ covering one side of the bipartition. This theorem admits a well-known algorithmic proof involving the repeated search of…

We consider the problem of finding a bijection between the sets of alternating sign matrices and of totally symmetric self complementary plane partitions, which can be reformulated using Gog and Magog triangles. In a previous work we…

We unify and extend previous bijections on plane quadrangulations to bipartite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different…

In this paper, we give a direct construction for a set of dice realizing any given tournament $T$. The construction for a tournament with $n$ vertices requires a number of sides on the order of $n$, which appears to be the best general…

A tournament is a directed graph resulting from an orientation of the complete graph; so, if $M$ is a tournament's adjacency matrix, then $M + M^T$ is a matrix with $0$s on its diagonal and all other entries equal to $1$. An outstanding…

We prove a conjecture by Aboulker, Charbit and Naserasr by showing that every oriented graph in which the out-neighborhood of every vertex induces a transitive tournament can be partitioned into two acyclic induced subdigraphs. We prove…

We study oriented graphs whose Hermitian adjacency matrices of the second kind have few eigenvalues. We give a complete characterization of the oriented graphs with two distinct eigenvalues, showing that there are only four such graphs. We…

We characterise the classes of tournaments with tractable first-order model checking. For every hereditary class of tournaments $\mathcal T$, first-order model checking is either fixed parameter tractable or $\textrm{AW}[*]$-hard. This…

The paper presents a hierarchical Bayesian model for simultaneous inference of tournament graphs and informant error. From multiple informant reports or measurement instrument outputs, the model estimates the structure of a criterion (i.e.,…

An out-branching $B^+_u$ (in-branching $B^-_u$) in a digraph $D$ is a connected spanning subdigraph of $D$ in which every vertex except the vertex $u$, called the root, has in-degree (out-degree) one. It is well-known that there exists a…

We introduce a game on graphs. By a theorem of Zermelo, each instance of the game on a finite graph is determined. While the general decision problem on which player has a winning strategy in a given instance of the game is unsolved, we…

We further study sets of labeled dice in which the relation "is a better die than" is non-transitive. Focusing on sets with an additional symmetry we call "balance," we prove that sets of $n$ such $m$-sided dice exist for all $n,m \geq 3$.…