Task reassignments in 2D mesh-connected systems (2D-MSs) have been researched for several decades. We propose a hierarchical 2D mesh-connected system (2D-HMS) in order to exploit the regular nature of a 2D-MS. In our approach priority-based task assignments and reassignments in a 2D-HMS are represented by tableaux and their algorithms. We show how task relocations for a priority-based task reas...

Given a graph G = (V,E), two players, Alice and Bob, alternate their turns in choosing uncoloured vertices to be coloured. Whenever an uncoloured vertex is chosen, it is coloured by the least positive integer not used by any of its coloured neighbours. Alice’s goal is to minimize the total number of colours used in the game, and Bob’s goal is to maximize it. The game Grundy number of G is the n...

We prove a conjecture of Knutson asserting that the Schubert structure constants of the cohomology ring of a two-step flag variety are equal to the number of puzzles with specified border labels that can be created using a list of eight puzzle pieces. As a consequence, we obtain a puzzle formula for the Gromov-Witten invariants defining the small quantum cohomology ring of a Grassmann variety o...

Résumé. Cet article décrit la génération automatique et l’utilisation d’une base de patterns pour le go 19x19. La représentation utilisée est celle des K plus proches voisins. Les patterns sont engendrés en parcourant des parties de professionnels. Les probabilités d’appariement et de jeu des patterns sont également estimées à ce moment là. La base créée est intégrée dans un programme existant,...

We give a backward jeu de taquin slide analogue on semistandard reverse composition tableaux. These tableaux were first studied by Haglund, Luoto, Mason and van Willigenburg when defining quasisymmetric Schur functions. Our algorithm for performing backward jeu de taquin slides on semistandard reverse composition tableaux results in a natural operator on compositions that we call the jdt operat...

The Wronskian associates to d linearly independent polynomials of degree at most n, a non-zero polynomial of degree at most d(n−d). This can be viewed as giving a flat, finite morphism from the Grassmannian Gr(d, n) to projective space of the same dimension. In this paper, we study the monodromy groupoid of this map. When the roots of the Wronskian are real, we show that the monodromy is combin...