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

2015/09/30 by José Aliste-Prieto, Aliste-Prieto, José, Anna de Mier +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1509.09210

arxiv created 2015/09/30 · arxiv updated 2015/10/01

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 U_k-polynomial, which is a restricted version of U-polynomial, and construct with the help of solutions of the Prouhet-Tarry-Escott problem, non-isomorphic trees with the same U_k-polynomial for any given k. By doing so, we also find a new class of trees that are distinguished by the U-polynomial up to isomorphism.

Related

• On the smallest trees with the same restricted U-polynomial and the\n rooted U-polynomial
• Chromatic symmetric functions and polynomial invariants of trees
• A rooted variant of Stanley's chromatic symmetric function
• Symmetric Chromatic Polynomial of Trees
• A tree distinguishing polynomial