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

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-...

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Bibliographic Details
Published in:Discrete mathematics Vol. 340; no. 6; pp. 1435 - 1441
Main Authors: Aliste-Prieto, José, de Mier, Anna, Zamora, José
Format: Journal Article Publication
Language:English
Published: Elsevier B.V 01.06.2017
Subjects:
05 Combinatorics
05C Graph theory
05E Algebraic combinatorics
[formula omitted]-polynomial
Chromatic symmetric function
Classificació AMS
Combinatorial analysis
Combinatòria
Graph polynomials
Matemàtica discreta
Matemàtiques i estadística
Polinomis
Polynomials
Prouhet–Tarry– Escott problem
UU-polynomial
Àrees temàtiques de la UPC
Prouhet–Tarry– Escott problem
Graph polynomials
Chromatic symmetric function
U-polynomial
ISSN:0012-365X, 1872-681X
Online Access:Get full text
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Summary: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.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2016.09.019