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 kk, non...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/112678 |
| Acceso en línea: | https://hdl.handle.net/2117/112678 https://dx.doi.org/10.1016/j.disc.2016.09.019 |
| Access Level: | acceso abierto |
| Palabra clave: | Polynomials Combinatorial analysis Chromatic symmetric function UU-polynomial Prouhet–Tarry– Escott problem Graph polynomials Polinomis Combinatòria Classificació AMS::05 Combinatorics::05C Graph theory Classificació AMS::05 Combinatorics::05E Algebraic combinatorics Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| Sumario: | 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 kk, 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. |
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