1.6k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Centre National de la Recherche ScientifiqueFR327 papers
- Université de BordeauxFR175 papers
- Institut National de Physique Nucléaire et de Physique des ParticulesFR130 papers
- Laboratoire de Physique des deux infinis BordeauxFR129 papers
- Commissariat à l'Énergie Atomique et aux Énergies AlternativesFR118 papers
- Institut de Mathématiques de BordeauxFR93 papers
- École PolytechniqueFR72 papers
- Observatoire de ParisFR72 papers
- Laboratoire Leprince-RinguetFR66 papers
- Astrophysique, Instrumentation et ModélisationFR64 papers
- Université Montpellier 263 papers
- Stanford UniversityUS62 papers
37 papers · 1 filter
Quasi-symmetric functions as polynomial functions on Young diagrams
Jean-Christophe Aval, Valentin Féray, Jean-Christophe Novelli +1
We determine the most general form of a smooth function on Young diagrams, that is, a polynomial in the interlacing or multirectangular coordinates whose value depends only on the…
A Structure Theorem for Small Sumsets in Nonabelian Groups
Oriol Serra, Gilles Zémor
Let G be an arbitrary finite group and let S and T be two subsets such that |S|>1, |T|>1, and |TS|< |T|+|S|< |G|-1. We show that if |S|< |G|-4|G|^{1/2}+1 then either S is a geometr…
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…
Geometric grid classes of permutations
Michael H. Albert, M. D. Atkinson, Mathilde Bouvel +2
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Us…
On the importance sampling of self-avoiding walks
Mireille Bousquet-Mélou
In a 1976 paper published in Science, Knuth presented an algorithm to sample (non-uniform) self-avoiding walks crossing a square of side k. From this sample, he constructed an esti…
Combinatorial Variations on Cantor's Diagonal
Srečko Brlek, Jean-Philippe Labbé, Michel Mendès France
We discuss counting problems linked to finite versions of Cantor's diagonal of infinite tableaux. We extend previous results of [2] by refining an equivalence relation that reduces…
Weakly directed self-avoiding walks
Axel Bacher, Mireille Bousquet-Mélou
We define a new family of self-avoiding walks (SAW) on the square lattice, called weakly directed walks. These walks have a simple characterization in terms of the irreducible brid…
Counting permutations with no long monotone subsequence via generating trees and the kernel method
Mireille Bousquet-Mélou
We recover Gessel's determinantal formula for the generating function of permutations with no ascending subsequence of length m+1. The starting point of our proof is the recursive…
Zonal polynomials via Stanley's coordinates and free cumulants
Valentin Feray, Piotr Śniady
We study zonal characters which are defined as suitably normalized coefficients in the expansion of zonal polynomials in terms of power-sum symmetric functions. We show that the zo…
Counting colored planar maps: algebraicity results
Olivier Bernardi, Mireille Bousquet-Mélou
We address the enumeration of properly q-colored planar maps, or more precisely, the enumeration of rooted planar maps M weighted by their chromatic polynomial χ_M(q) and counted b…
Partial Jucys-Murphy elements and star factorizations
Valentin Feray
In this paper, we look at the number of factorizations of a given permutation into star transpositions. In particular, we give a natural explanation of a hidden symmetry, answering…
On the symmetry of the partition function of some square ice models
Jean-Christophe Aval
We consider the partition function Z(N;x_1,...,x_N,y_1,...,y_N) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all i…
(2+2)-free posets, ascent sequences and pattern avoiding permutations
Mireille Bousquet-Mélou, Anders Claesson, Mark Dukes +1
We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2+2)-free posets and a certain class of involutions (or chord diagrams), a…
Families of prudent self-avoiding walks
Mireille Bousquet-Mélou
A self-avoiding walk (SAW) on the square lattice is prudent if it never takes a step towards a vertex it has already visited. Prudent walks differ from most classes of SAW that hav…
Lower bounds for measurable chromatic numbers
Christine Bachoc, Gabriele Nebe, Fernando Mario de Oliveira Filho +1
The Lovasz theta function provides a lower bound for the chromatic number of finite graphs based on the solution of a semidefinite program. In this paper we generalize it so that i…
Proof of Stanley's conjecture about irreducible character values of the symmetric group
Valentin Féray
R. Stanley has found a nice combinatorial formula for characters of irreducible representations of the symmetric group of rectangular shape. Then, he has given a conjectural genera…
Three osculating walkers
Mireille Bousquet-Mélou
We consider three directed walkers on the square lattice, which move simultaneously at each tick of a clock and never cross. Their trajectories form a non-crossing configuration of…
Generating functions for generating trees
Cyril Banderier, Philippe Flajolet, Daniele Gardy +3
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the n…
An iterative-bijective approach to generalizations of Schur's theorem
Sylvie Corteel, Jeremy Lovejoy
We start with a bijective proof of Schur's theorem due to Alladi and Gordon and describe how a particular iteration of it leads to some very general theorems on colored partitions.…
Walks confined in a quadrant are not always D-finite
Mireille Bousquet-Melou, Marko Petkovsek
We consider planar lattice walks that start from a prescribed position, take their steps in a given finite subset of Z^2, and always stay in the quadrant x >= 0, y >= 0. We first g…
Refined Restricted Permutations Avoiding Subsets of Patterns of Length Three
Toufik Mansour, Aaron Robertson
Define to be the set of permutations of with exactly fixed points which avoid all patterns in . We enumerate , $T \subsete…
Ideals of Quasi-Symmetric Functions and Super-Covariant Polynomials for S_n
J. -C. Aval, F. Bergeron, N. Bergeron
The aim of this work is to study the quotient ring R_n of the ring Q[x_1,...,x_n] over the ideal J_n generated by non-constant homogeneous quasi-symmetric functions. We prove here…
Coloured permutations containing and avoiding certain patterns
T. Mansour
Following Mansour, let be the set of all coloured permutations on the symbols with colours , which is the analogous of the symmetric group when r…
Schur Partial Derivative Operators
Jean-Christophe Aval, Nantel Bergeron
A lattice diagram is a finite list L=((p_1,q_1),...,(p_n,q_n) of lattice cells. The corresponding lattice diagram determinant is Δ_L(X;Y)=\det \| x_i^{p_j}y_i^{q_j} \|. These latti…