6 papers
Cyclic sieving phenomena for trees and tree-rooted maps
Mireille Bousquet-Mélou, Christian Krattenthaler
We prove cyclic sieving phenomena satisfied by corner-rooted plane trees (alias ordered trees). The sets of rooted plane trees that we consider are: (1) all trees with nodes; (…
The Ising model on cubic maps: arbitrary genus
Mireille Bousquet-Mélou, Ariane Carrance, Baptiste Louf
We design a recursive algorithm to compute the partition function of the Ising model, summed over cubic maps with fixed size and genus. The algorithm runs in polynomial time, which…
The ascent lattice on Dyck paths
Jean-Luc Baril, Mireille Bousquet-Mélou, Sergey Kirgizov +1
In the Stanley lattice defined on Dyck paths of size , cover relations are obtained by replacing a valley by a peak . We investigate a greedy version of this lattice, f…
Culminating paths
Mireille Bousquet-Mélou, Yann Ponty
Let a and b be two positive integers. A culminating path is a path of Z^2 that starts from (0,0), consists of steps (1,a) and (1,-b), stays above the x-axis and ends at the highest…
The density of the ISE and local limit laws for embedded trees
Mireille Bousquet-Mélou, Svante Janson
It has been known for a few years that the occupation measure of several models of embedded trees converges, after a suitable normalization, to the random measure called ISE (Integ…
Limit laws for embedded trees. Applications to the integrated superBrownian excursion
Mireille Bousquet-Mélou
We study three families of labelled plane trees. In all these trees, the root is labelled 0, and the labels of two adjacent nodes differ by or -1. One part of the paper is d…