2016/01/17 by Guo-Niu Han, Huan Xiong, Han, Guo-Niu +1
Mathematics · #05A15 #05A17 #05A19 #05E05 #05E10 #11P81 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1601.04369
openalex publication_date 2016/01/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In 2009, the first author proved the Nekrasov-Okounkov formula on hook lengths for integer partitions by using an identity of Macdonald in the framework of type \widetilde A affine root systems, and conjectured that some summations over the set of all partitions of size n are always polynomials in n. This conjecture was generalized and proved by Stanley. Recently, Pétréolle derived two Nekrasov-Okounkov type formulas for \widetilde C and \widetilde C \check which involve doubled distinct and self-conjugate partitions. Inspired by all those previous works, we establish the polynomiality of some hook-content summations for doubled distinct and self-conjugate partitions.