相关论文: Coxeter tournaments
We prove the celebrated representation theorem of Andreka-Resek-Thompson, together with its polyadic analogue by Ferenczi, using games as introduced in algebraic logic by Hirsch and Hodkinson. We also show that atomic algebras are…
We compute the equivariant K-theory with integer coefficients of an equivariantly formal isotropy action, subject to natural hypotheses which cover the three major classes of known examples. The proof proceeds by constructing a map of…
We continue to explore the ways in which high-level topological connections arise from connections between fundamental features of the spaces, in this case focusing on star-selection principles in Pixley-Roy hyperspaces and uniform spaces.…
A version of the Hodge-Riemann relations for valuations was recently conjectured and proved in several special cases by the first-named author. The Lefschetz operator considered there arises as either the product or the convolution with the…
We compute the MU-based syntomic cohomologies, mod $(p,v_1,\cdots,v_{n+1})$, of all $\mathbb{E}_1$-MU-algebra forms of connective Morava K-theory k(n). As qualitative consequences, we deduce the Lichtenbaum--Quillen conjecture, telescope…
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…
We describe the cone of deformations of a Coxeter permutahedron, or equivalently, the nef cone of the toric variety associated to a Coxeter complex. This family of polytopes contains polyhedral models for the Coxeter-theoretic analogs of…
Sumner's universal tournament conjecture states that any tournament on $2n-2$ vertices contains any directed tree on $n$ vertices. In this paper we prove that this conjecture holds for all sufficiently large $n$. The proof makes extensive…
The Alesker product turns the space of smooth translation-invariant valuations on convex bodies into a commutative associative unital algebra, satisfying Poincar\'e duality and the hard Lefschetz theorem. In this article, a version of the…
Global permutation patterns have recently been shown to characterize important properties of a Coxeter group. Here we study global patterns in the context of signed permutations, with both characterizing and enumerative results.…
In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe…
We enlarge a Coxeter group into a category, with one object for each finite parabolic subgroup, encoding the combinatorics of double cosets. This category, the singular Coxeter monoid, is connected to the geometry of partial flag varieties.…
We analyse a mathematical model of seeding for sports contests with round-robin qualifying tournaments. The standard seeding system based on coefficients measuring the historical performance of the teams is shown to be unfair as it might…
A large variety of cohomology theories is derived from complex cobordism MU^*(-) by localizing with respect to certain elements or by killing regular sequences in MU_*. We study the relationship between certain pairs of such theories which…
Tournament ranking is a function that assigns each vertex of a tournament (i.e., a directed graph without loops, in which each pair of different vertexes is connected by exactly one arc) a number called the rank of the vertex. One of…
The Erd\H{o}s-Hajnal Conjecture states that for every $H$ there exists a constant $\epsilon(H)>0$ such that every graph $G$ that does not contain $H$ as an induced subgraph contains a clique or a stable set of size at least…
Motivated by the home-field advantage in sports, we propose a generalized Bradley--Terry model that incorporates covariate information for paired comparisons. It has an $n$-dimensional merit parameter $\bs{\beta}$ and a fixed-dimensional…
This paper examines and strengthens the Cuntz-Thomsen picture of equivariant Kasparov theory for arbitrary second-countable locally compact groups, in which elements are given by certain pairs of cocycle representations between C*-dynamical…
In cooperative game theory, associated games allow for providing meaningful characterizations of solution concepts. Moreover, generalized values allow computing an influence or power index of each coalition in a game. In this paper, we view…
In this paper the complexity of provability of polarized additive, multiplicative, and exponential formulas in the (initial) Cockett-Seely polarized game logic is discussed. The complexity is ultimately based on the complexity of finding a…