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

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9 Citations (Scopus)

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 k, 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.

Original languageEnglish
Pages (from-to)1435-1441
Number of pages7
JournalDiscrete Mathematics
Volume340
Issue number6
DOIs
Publication statusPublished - 1 Jun 2017

Keywords

  • Chromatic symmetric function
  • Graph polynomials
  • Prouhet–Tarry– Escott problem
  • U-polynomial

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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