53 citations · 134 across the 5 of their papers we have counts for
6 papers
Bijections for faces of braid-type arrangements
Olivier Bernardi
We establish a general bijective framework for encoding faces of some classical hyperplane arrangements. Precisely, we consider hyperplane arrangements in whose hype…
Intervals in the greedy Tamari posets
Mireille Bousquet-Mélou, Frédéric Chapoton
We consider a greedy version of the -Tamari order defined on -Dyck paths, recently introduced by Dermenjian. Inspired by intriguing connections between intervals in the ordin…
Counting quadrant walks via Tutte's invariant method
Olivier Bernardi, Mireille Bousquet-Mélou, Kilian Raschel
In the 1970s, William Tutte developed a clever algebraic approach, based on certain "invariants", to solve a functional equation that arises in the enumeration of properly colored…
Counting quadrant walks via Tutte's invariant method (extended abstract)
O Bernardi, M Bousquet-Mélou, Kilian Raschel
In the 1970s, Tutte developed a clever algebraic approach, based on certain "invariants" , to solve a functional equation that arises in the enumeration of properly colored triangu…
A Bijection between well-labelled positive paths and matchings
Olivier Bernardi, Bertrand Duplantier, Philippe Nadeau
A well-labelled positive path of size n is a pair (p,σ) made of a word p=p_1p_2...p_{n-1} on the alphabet {-1, 0,+1} such that the sum of the letters of any prefix is non-negative,…
Solution to a combinatorial puzzle arising from Mayer's theory of cluster integrals
Olivier Bernardi
Mayer's theory of cluster integrals allows one to write the partition function of a gas model as a generating function of weighted graphs. Recently, Labelle, Leroux and Ducharme ha…