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- Viviane Pons
- IJAC
- 2013

We give a combinatorial interpretation of a Pieri formula for double Grothendieck polynomials in terms of an interval of the Bruhat order. Another description had been given by Lenart and Postnikov in terms of chain enumerations. We use Lascoux's interpretation of a product of Grothendieck polynomials as a product of two kinds of generators of the 0-Hecke… (More)

We have developed a patch implementing multivariate polynomials seen as a multi-base algebra. The patch is to be released into the software Sage and can already be found within the Sage-Combinat distribution. One can use our patch to define a polynomial in a set of indexed variables and expand it into a linear basis of the multivariate polynomials. So far,… (More)

We introduce new combinatorial objects, the interval-posets, that encode intervals of the Tamari lattice. We then find a combinatorial interpretation of the bilinear form that appears in the functional equation of Tamari intervals described by Chapoton. Thus, we retrieve this functional equation and prove that the polynomial recursively computed from the… (More)

The FindStat project provides an online platform for mathematicians, particularly for combinatorialists, to gather information about combinatorial statistics and their relations. As of January 2014, the FindStat database contains 173 statistics on 17 combinatorial collections. Combinatorial statistics arise naturally all over mathematics. Before we give the… (More)

We use a recently introduced combinatorial object, the interval-poset, to describe two bijections on intervals of the Tamari lattice. Both bijections give a combinatorial proof of some previously known results. The first one is an inner bijection between Tamari intervals that exchanges the initial rise and lower contacts statistics. Those were introduced by… (More)

Viviane Pons Combinatoire algébrique liée aux ordres sur les permutations

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