Related papers: Coxeter tournaments
A celebrated unresolved conjecture of Erd\H{o}s and Hajnal states that for every undirected graph $H$ there exists $\epsilon(H)>0$ such that every undirected graph on $n$ vertices that does not contain $H$ as an induced subgraph contains a…
We study the projective objects in an exact category naturally associated to a Coxeter system. We discuss an analog of the Kazhdan-Lusztig conjecture and show how it follows from a "genericity" conjecture and how the latter follows from a…
We write the master equation describing the Parrondo's games as a consistent discretization of the Fokker--Planck equation for an overdamped Brownian particle describing a ratchet. Our expressions, besides giving further insight on the…
Seymour's distance two conjecture states that in any digraph there exists a vertex (a "Seymour vertex") that has at least as many neighbors at distance two as it does at distance one. We explore the validity of probabilistic statements…
We settle a question of Bressoud concerning the existence of an explicit bijection from a class of oriented square-ice graphs to a class of tournaments. We give an algorithm constructing such a bijection.
A conjecture of Alon, Pach and Solymosi, which is equivalent to the celebrated Erd\H{o}s-Hajnal Conjecture, states that for every tournament $S$ there exists $\epsilon(S)>0$ such that if $T$ is an $n$-vertex tournament that does not…
In this note, we show how positional strategies for $k$-pebble games have a natural representation as certain presheaves. These representations correspond exactly to the sheaf-theoretic models of contextuality introduced by…
The aim of this paper is to use the methods and results of symplectic homogenization (see [V4]) to prove existence of periodic orbits and invariant measures with rotation number depending on the differential of the Homogenized Hamiltonian.…
The Erdos-Moser theorem (EM) states that every infinite tournament has an infinite transitive subtournament. This principle plays an important role in the understanding of the computational strength of Ramsey's theorem for pairs (RT^2_2) by…
Negative dependence of sequences of random variables is often an interesting characteristic of their distribution, as well as a useful tool for studying various asymptotic results, including central limit theorems, Poisson approximations,…
Motivated by work of Coxeter (1957), we study a class of algebras associated to Coxeter groups, which we term 'generalized nil-Coxeter algebras'. We construct the first finite-dimensional examples other than usual nil-Coxeter algebras;…
This paper generalizes L.S. Shapley's celebrated value allocation theory on coalition games by discovering and applying a fundamental connection between stochastic path integration driven by canonical time-reversible Markov chains and…
The poset of copies of a relational structure ${\mathbb X}$ is the partial order ${\mathbb P} ({\mathbb X} ) := \langle \{ Y \subset X: {\mathbb Y} \cong {\mathbb X}\}, \subset \rangle$ and each similarity of such posets (e.g. isomorphism,…
We study algebraic K-theory, syntomic cohomology, and prismatic cohomology of Cartier smooth rings. As an application, we provide an alternative proof of Kelly-Morrow's generalization of the Geisser-Levine theorem computing $p$-adic…
We give presentations, by means of diagrammatic generators and relations, of the analogues of the Temperley-Lieb algebras associated as Hecke algebra quotients to Coxeter graphs of type B and $D$. This generalizes Kauffman's diagram…
First we introduce the Bailleul-Hoshino's result [4], which links the theory of regularity structures and the paracontrolled calculus. As an application of their result, we give another algebraic proof of the multicomponent commutator…
We introduce for any Poisson algebra a bicomplex of free Poisson modules, and use it to show that the Poisson cohomology theory introduced in the paper "[M. Flato, M. Gerstenhaber and A. A. Voronov, Cohomology and Deformation of Leibniz…
In this paper, we generalize Schur-Weyl duality and Morita Theorem on associative algebras to those on associative $H$-pseudoalgebras. Meanwhile, we get a plenty of associative $H$-pseudoalgebras over a cocommutative Hopf algebra $H$.
We give formulas for the second and third integral homology of an arbitrary finitely generated Coxeter group, solely in terms of the corresponding Coxeter diagram. The first of these calculations refines a theorem of Howlett, while the…
Using the notion of Mahonian statistic on acyclic posets, we introduce a $q$-analogue of the $h$-polynomial of a simple generalized permutohedron. We focus primarily on the case of nestohedra and on explicit computations for many…