20 citations · 88 across the 33 of their papers we have counts for
35 papers
Cluster parking functions II: -dihedral sieving via diagonal coinvariants
Matthieu Josuat-Vergès
In a previous work, we defined the complex of cluster parking functions. On one side, they encode the type-refined enumeration of faces of the cluster complex, and on the other sid…
Homology character of the parabolic coset poset
Theo Douvropoulos, Matthieu Josuat-Vergès
Motivated by the analogy with the Coxeter complex on one side, and parking functions on the other side, we study the poset of parabolic cosets in a finite Coxeter group. We show th…
Automorphisms of the generalized cluster complex
Matthieu Josuat-Vergès
It is proved that the generalized cluster complex defined by Fomin and Reading has a dihedral symmetry. Together with diagram symmetries, they generate its automorphism group. A co…
Cluster parking functions
Theo Douvropoulos, Matthieu Josuat-Vergès
The cluster complex on one hand, parking functions on the other hand, are two combinatorial (po)sets that can be associated to a finite real reflection group. Cluster parking funct…
Combinatorics of the Delta conjecture at q=-1
Sylvie Corteel, Matthieu Josuat-Vergès, Anna Vanden Wyngaerd
In the context of the shuffle theorem, many classical integer sequences appear with a natural refinement by two statistics and : for example the Catalan and Schröder numbers…
The Generalized Cluster Complex: Refined Enumeration of Faces and Related Parking Spaces
Theo Douvropoulos, Matthieu Josuat-Vergès
The generalized cluster complex was introduced by Fomin and Reading, as a natural extension of the Fomin-Zelevinsky cluster complex coming from finite type cluster algebras. In thi…
Koszulity of dual braid monoid algebras via cluster complexes
Matthieu Josuat-Vergès, Philippe Nadeau
The dual braid monoid was introduced by Bessis in his work on complex reflection arrangements. The goal of this work is to show that Koszul duality provides a nice interplay betwee…
Some properties of the parking function poset
Bérénice Delcroix-Oger, Matthieu Josuat-Vergès, Lucas Randazzo
In 1980, Edelman defined a poset on objects called the noncrossing 2-partitions. They are closely related with noncrossing partitions and parking functions. To some extent, his def…
Combinatorial proof of an identity on Genocchi numbers
Beáta Bényi, Matthieu Josuat-Vergès
In this note we present a combinatorial proof of an identity involving poly-Bernoulli numbers and Genocchi numbers. We introduce the combinatorial objects, barred Callan sequen…
Extensions of partial cyclic orders and consecutive coordinate polytopes
Arvind Ayyer, Matthieu Josuat-Vergès, Sanjay Ramassamy
We introduce several classes of polytopes contained in and cut out by inequalities involving sums of consecutive coordinates. We show that the normalized volumes of these…
Noncrossing partitions, Bruhat order and the cluster complex
Philippe Biane, Matthieu Josuat-Vergès
We introduce two order relations on finite Coxeter groups which refine the absolute and the Bruhat order, and establish some of their main properties. In particular we study the re…
Δ-cumulants in terms of moments
Matthieu Josuat-Vergès
The Δ-convolution of real probability measures, introduced by Bożejko, generalizes both free and boolean convolutions. It is linearized by the Δ-cumulants, and Yoshida gave a combi…
Minimal factorizations of a cycle: a multivariate generating function
Philippe Biane, Matthieu Josuat-Vergès
It is known that the number of minimal factorizations of the long cycle in the symmetric group into a product of cycles of given lengths has a very simple formula: it is $n^{k-…
A q-analog of Schläfli and Gould identities on Stirling numbers
Matthieu Josuat-Vergès
Stirling numbers of both kinds are linked to each other via two combinatorial identities due to Schläfli and Gould. Using q-analogs of Stirling numbers defined as inversion generat…
Subalgebras of Solomon's descent algebra based on alternating runs
Matthieu Josuat-Vergès, C. Y. Amy Pang
The number of alternating runs is a natural permutation statistic. We show it can be used to define some commutative subalgebras of the symmetric group algebra, and more precisely…
Free cumulants, Schröder trees, and operads
Matthieu Josuat-Vergès, Frédéric Menous, Jean-Christophe Novelli +1
The functional equation defining the free cumulants in free probability is lifted successively to the noncommutative Faà di Bruno algebra, and then to the group of a free operad ov…
Stammering tableaux
Matthieu Josuat-Vergès
The PASEP (Partially Asymmetric Simple Exclusion Process) is a probabilistic model of moving particles, which is of great interest in combinatorics, since it appeared that its part…
Generalized Dyck tilings
Matthieu Josuat-Vergès, Jang Soo Kim
Recently, Kenyon and Wilson introduced Dyck tilings, which are certain tilings of the region between two Dyck paths. The enumeration of Dyck tilings is related with hook formulas f…
Refined enumeration of noncrossing chains and hook formulas
Matthieu Josuat-Vergès
In the combinatorics of finite finite Coxeter groups, there is a simple formula giving the number of maximal chains of noncrossing partitions. It is a reinterpretation of a result…
Flag statistics from the Ehrhart series of multi-hypersimplices
Guo-Niu Han, Matthieu Josuat-Vergès
It is known that the normalized volume of standard hypersimplices (defined as some slices of the unit hypercube) are the Eulerian numbers. More generally, a recent conjecture of St…
Derivatives of the tree function
Matthieu Josuat-Vergès
We study some sequences of polynomials that appear when we consider the successive derivatives of the tree function (or Lambert's W function). We show in particular that they are r…
A generalization of Euler numbers to finite Coxeter groups
Matthieu Josuat-Vergès
It is known that Euler numbers, defined as the Taylor coefficients of the tangent and secant functions, count alternating permutations in the symmetric group. Springer defined a ge…
Cumulants of the q-semicircular law, Tutte polynomials, and heaps
Matthieu Josuat-Vergès
The q-semicircular distribution is a probability law that interpolates between the Gaussian law and the semicircular law. There is a combinatorial interpretation of its moments in…
Combinatorics of the permutation tableaux of type B
Sylvie Corteel, Matthieu Josuat-Vergès, Jang Soo Kim
Permutation tableaux are combinatorial objects related with permutations and various statistics on them. They appeared in connection with total positivity in Grassmannians, and sta…