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
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
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=85028256259&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2016.09.019
DO - 10.1016/j.disc.2016.09.019
M3 - Article
AN - SCOPUS:85028256259
SN - 0012-365X
VL - 340
SP - 1435
EP - 1441
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 6
ER -