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The Hopf algebra of integer binary relations
Vincent Pilaud, Viviane Pons
We construct a Hopf algebra on integer binary relations that contains under the same roof several well-known Hopf algebras related to the permutahedra and the associahedra: the Mal…
The Rise-Contact involution on Tamari intervals
Viviane Pons
We describe an involution on Tamari intervals and m-Tamari intervals. This involution switches two sets of statistics known as the "rises" and the "contacts" and so proves an open…
Counting smaller trees in the Tamari order
Viviane Pons, Gregory Chatel
We introduce new 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 fun…
Multivariate Polynomials in Sage
Viviane Pons
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…