On trees with the same restricted U-polynomial and the Prouhet–Tarry–Escott problem

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Title:	On trees with the same restricted U-polynomial and the Prouhet–Tarry–Escott problem
Author:	Aliste Prieto, José; Mier Vinué, Anna de; Zamora, José
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
Abstract:	This paper focuses on the well-known problem due to Stanley of whether two non-isomorphic trees can have the same U-polynomial (or, equivalently, the same chromatic symmetric function). We consider the Uk-polynomial, which is a restricted version of U-polynomial, and construct, for any given kk, non-isomorphic trees with the same Uk-polynomial. These trees are constructed by encoding solutions of the Prouhet–Tarry–Escott problem. As a consequence, we find a new class of trees that are distinguished by the U-polynomial up to isomorphism.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria -Polynomials -Combinatorial analysis -Chromatic symmetric function -UU-polynomial -Prouhet–Tarry– Escott problem -Graph polynomials -Polinomis -Combinatòria -Classificació AMS::05 Combinatorics::05C Graph theory -Classificació AMS::05 Combinatorics::05E Algebraic combinatorics
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Document type:	Article - Submitted version Article
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