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Our main result here is that the specialization at $t=1/q$ of the $Q_{km,kn}$ operators studied in [4] may be given a very simple plethystic form. This discovery yields elementary and direct derivations of several identities relating these…
Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an…
We consider the unconstrained traveling tournament problem, a sports timetabling problem that minimizes traveling of teams. Since its introduction about 20 years ago, most research was devoted to modeling and reformulation approaches. In…
Let $M(n)$ denote the number of distinct entries in the $n \times n$ multiplication table. The function $M(n)$ has been studied by Erd\H{o}s, Tenenbaum, Ford, and others, but the asymptotic behaviour of $M(n)$ as $n \to \infty$ is not known…
How many ways, exactly, can a Chess King, always moving forward (i.e. with steps [1,0],[0,1],[1,1]) walk to [100000,200000]? Thanks to the amazing Apagodu-Zeilberger extension of the Almkvist-Zeilberger algorithm, adapted in this article…
It is proved that the number of partitions of n with odd mex and k parts that aren't ones equals the number of partitions of n with nonnegative crank and k parts that aren't ones..
The Tsetlin library is a well-studied Markov chain on the symmetric group $S_n$. It has stationary distribution $\pi(\sigma)$ the Luce model, a nonuniform distribution on $S_n$, which appears in psychology, horse race betting, and…
We use analytic and numerical methods to obtain the solution of the Q-ball equation of motion. In particular, we show that the profile function of the three-dimensional Q-ball can be accurately approximated by the symmetrized Woods-Saxon…
Multi-agent learning algorithms have been shown to display complex, unstable behaviours in a wide array of games. In fact, previous works indicate that convergent behaviours are less likely to occur as the total number of agents increases.…
Motion polynomials are a specific type of polynomial over a Clifford algebra that can conveniently describe rational motions. There exists an algorithm for the factorization of motion polynomials that works in generic cases. It hinges on…
From a geometric viewpoint, billiard trajectories and geodesics are related by mutual approximation results. In one direction, it is known that every geodesic curve in the boundary of a smooth convex body can be approximated by a sequence…
We extend work of McKay, Morse, and Wilf by giving exact formulas and asymptotic formulas for the number of skew Young tableaux T in two situations: (1) the "inside shape" and total number of cells of T are fixed, and (2) the inside shape…
We introduce a homological approach to exhibiting instances of Stembridge's q=-1 phenomenon. This approach is shown to explain two important instances of the phenomenon, namely that of partitions whose Ferrers diagrams fit in a rectangle of…
We consider Chess played on an $m \times n$ board (with $m$ and $n$ arbitrary positive integers), with only the two kings and the white rook remaining, but placed at arbitrary positions. Using the symbolic finite state method, developed by…
We study properties of quantum strategies, which are complete specifications of a given party's actions in any multiple-round interaction involving the exchange of quantum information with one or more other parties. In particular, we focus…
Let R be a commutative ring and let n,m be two positive integers. Let be the polynomial ring in m x n commuting independent variables R. The symmetric group on n letters acts diagonally on A(n,m). We give generators and relations of the…
Changing some of its parameters over time is a paradigmatic way of driving an otherwise isolated many-body quantum system out of equilibrium, and a vital ingredient for building quantum computers and simulators. Here, we further develop a…
This paper addresses zero-sum ``turn'' games, in which only one player can make decisions at each state. We show that pure saddle-point state-feedback policies for turn games can be constructed from dynamic programming fixed-point equations…
Given a planar oval, consider the maximal area of inscribed $n$-gons resp. the minimal area of circumscribed $n$-gons. One obtains two sequences indexed by $n$, and one of Dowker's theorems states that the first sequence is concave and the…
Borisov, Mamaev and Kilin have recently found certain Poisson structures with respect to which the reduced and rescaled systems of certain non-holonomic problems, involving rolling bodies without slipping, become Hamiltonian, the…