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7 papers · 2 filters
Structure coefficients of the Hecke algebra of
Omar Tout
The Hecke algebra of the pair , where is the hyperoctahedral subgroup of , was introduced by James in 1961. It is a natural analogue of the center of th…
A natural stochastic extension of the sandpile model on a graph
Yao-ban Chan, Jean-François Marckert, Thomas Selig
We introduce a new model of a stochastic sandpile on a graph containing a sink. When unstable, a site sends one grain to each of its neighbours independently with probability $…
Parallelogram polyominoes, the sandpile model on a complete bipartite graph, and a q,t-Narayana polynomial
Mark Dukes, Yvan Le Borgne
We classify recurrent configurations of the sandpile model on the complete bipartite graph K_{m,n} in which one designated vertex is a sink. We present a bijection from these recur…
A multivariate hook formula for labelled trees
Valentin Féray, I. P. Goulden
Several hook summation formulae for binary trees have appeared recently in the literature. In this paper we present an analogous formula for unordered increasing trees of size r, w…
The vertical profile of embedded trees
Mireille Bousquet-Mélou, Guillaume Chapuy
Consider a rooted binary tree with n nodes. Assign with the root the abscissa 0, and with the left (resp. right) child of a node of abscissa i the abscissa i-1 (resp. i+1). We prov…
The representation of the symmetric group on m-Tamari intervals
Mireille Bousquet-Mélou, Guillaume Chapuy, Louis-François Préville-Ratelle
An m-ballot path of size n is a path on the square grid consisting of north and east unit steps, starting at (0,0), ending at (mn,n), and never going below the line {x=my}. The set…