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of 24
pro vyhledávání: '"Pétréolle , Mathias"'
We introduce a triangular array $\widehat{\sf L}^{(\alpha)}$ of 5-variable homogeneous polynomials that enumerate Laguerre digraphs (digraphs in which each vertex has out-degree 0 or 1 and in-degree 0 or 1) with separate weights for peaks, valleys, d
Externí odkaz:
http://arxiv.org/abs/2312.11081
Autor:
Pétréolle, Mathias, Sokal, Alan D.
Publikováno v:
European Journal of Combinatorics 92, 103235 (February 2021)
We introduce the generic Lah polynomials $L_{n,k}(\phi)$, which enumerate unordered forests of increasing ordered trees with a weight $\phi_i$ for each vertex with $i$ children. We show that, if the weight sequence $\phi$ is Toeplitz-totally positive
Externí odkaz:
http://arxiv.org/abs/1907.02645
We define an infinite sequence of generalizations, parametrized by an integer $m \ge 1$, of the Stieltjes--Rogers and Thron--Rogers polynomials; they arise as the power-series expansions of some branched continued fractions, and as the generating pol
Externí odkaz:
http://arxiv.org/abs/1807.03271
Autor:
Pétréolle, Mathias
In 2015, the author proved combinatorially character formulas expressing sums of the (formal) dimensions of irreducible representations of symplectic groups, refining some works of Nekrasov and Okounkov, Han, King, and Westbury. In this article, we o
Externí odkaz:
http://arxiv.org/abs/1612.03771
Autor:
Pétréolle, Mathias
In this paper, we study the generating function of cyclically fully commutative elements in Coxeter groups, which are elements such that any cyclic shift of theirs reduced decompositions remains a reduced expression of a fully commutative element. By
Externí odkaz:
http://arxiv.org/abs/1612.03764
The aim of this work is the study of the class of periodic parallelogram polyominoes, and two of its variantes. These objets are related to 321-avoiding affine permutations. We first provide a bijection with the set of triangles under Dyck paths. We
Externí odkaz:
http://arxiv.org/abs/1612.03759
Autor:
Pétréolle, Mathias, Sokal, Alan D.
Publikováno v:
In European Journal of Combinatorics February 2021 92
Autor:
Pétréolle, Mathias
In 2008, Han rediscovered an expansion of powers of Dedekind $\eta$ function due to Nekrasov and Okounkov by using Macdonald's identity in type $\widetilde{A}$. In this paper, we obtain new combinatorial expansions of powers of $\eta$, in terms of pa
Externí odkaz:
http://arxiv.org/abs/1505.01324
Autor:
Pétréolle, Mathias
In 2008, Han rediscovered an expansion of powers of Dedekind $\eta$ function attributed to Nekrasov and Okounkov (which was actually first proved the same year by Westbury) by using a famous identity of Macdonald in the framework of type $\widetilde{
Externí odkaz:
http://arxiv.org/abs/1505.01295