On trees with the same restricted U-polynomial and the Prouhet–Tarry–Escott problem
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Archivos
Fecha
2017-06
Profesor/a Guía
Facultad/escuela
Idioma
en
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Título del volumen
Editor
Elsevier B.V.
Nombre de Curso
Licencia CC
CC BY 4.0 DEED
Atribución 4.0 Internacional
Licencia CC
https://creativecommons.org/licenses/by/4.0/deed.es
Resumen
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. © 2016 Elsevier B.V.
Notas
Palabras clave
Chromatic symmetric function, Graph polynomials, Prouhet–Tarry– Escott problem, U-polynomial
Citación
Discrete Mathematics Volume 340, Issue 6, Pages 1435 - 14411 June 2017
DOI
10.1016/j.disc.2016.09.019