### 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 U_{k}-polynomial, which is a restricted version of U-polynomial, and construct, for any given k, non-isomorphic trees with the same U_{k}-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.

Idioma original | English |
---|---|

Páginas (desde-hasta) | 1435-1441 |

Número de páginas | 7 |

Publicación | Discrete Mathematics |

Volumen | 340 |

N.º | 6 |

DOI | |

Estado | Published - 1 jun 2017 |

### Huella dactilar

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Citar esto

*Discrete Mathematics*,

*340*(6), 1435-1441. https://doi.org/10.1016/j.disc.2016.09.019

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*Discrete Mathematics*, vol. 340, n.º 6, pp. 1435-1441. https://doi.org/10.1016/j.disc.2016.09.019

**On trees with the same restricted U-polynomial and the Prouhet–Tarry–Escott problem.** / Aliste-Prieto, José; de Mier, Anna; Zamora, José.

Resultado de la investigación: Article

TY - JOUR

T1 - On trees with the same restricted U-polynomial and the Prouhet–Tarry–Escott problem

AU - Aliste-Prieto, José

AU - de Mier, Anna

AU - Zamora, José

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

AB - 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.

KW - Chromatic symmetric function

KW - Graph polynomials

KW - Prouhet–Tarry– Escott problem

KW - U-polynomial

UR - http://www.scopus.com/inward/record.url?scp=85015628094&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2016.09.019

DO - 10.1016/j.disc.2016.09.019

M3 - Article

VL - 340

SP - 1435

EP - 1441

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 6

ER -