Mercredi 25 Mai

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Mercredi 25 Mai
Heure: 14:00 - 15:00
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: On the reconstruction of trees from their U-polynomial.
Description: José Aliste-Prieto The U-polynomial of a graph was introduced by Noble and Welsh as a generalization of some invariants coming from Knot theory. It also generalizes the chromatic symmetric function of Stanley. In this talk, we will consider the problem of whether there exist non-isomorphic trees
with the same U-polynomial (or,equivalently, with the same chromatic symmetric function).

We will survey what is know about the U-polynomial and this problem. In particular, we will show how to recover some classic invariants from the U-polynomial and we exhibit several subclasses of trees for which a solution of this problem is known. FInally, we construct some non-isomorphic trees with "almost" the same U-polynomial, based on solutions of an old problem in Number theory due to Prouhet-Tarry-Escott.