P-partition generating function equivalence of naturally labeled posets

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:170

Article

Liu, Ricky Ini¹  Weselcouch, Michael¹ 

[1] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

关键词: P-Partition;    Quasisymmetric function;    Combinatorial hopf algebra;   

DOI  :  10.1016/j.jcta.2019.105136

来源: Elsevier

【 摘 要 】

The P-partition generating function of a (naturally labeled) poset P is a quasisymmetric function enumerating order-preserving maps from P to Z(+). Using the Hopf algebra of posets, we give necessary conditions for two posets to have the same generating function. In particular, we show that they must have the same number of antichains of each size, as well as the same shape (as defined by Greene). We also discuss which shapes guarantee uniqueness of the P-partition generating function and give a method of constructing pairs of non-isomorphic posets with the same generating function. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free