CONGRUENCES FOR HAN’S GENERATING FUNCTION
by
Dan Collins
,
Sally Wolfe
BibTeX
@MISC{Collins_congruencesfor,
author = {Dan Collins and Sally Wolfe},
title = {CONGRUENCES FOR HAN’S GENERATING FUNCTION},
year = {}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
Abstract. For an integer t ≥ 1 and a partition λ, we let Ht(λ) be the multiset of hook lengths of λ which are divisible by t. Then, define aeven t (n) and aodd t (n) to be the number of partitions of n such that |Ht(λ) | is even or odd, respectively. In a recent paper, Han generalized the Nekrasov-Okounkov formula to obtain a generating function for at(n) = aeven t (n) − aodd t (n). We use this generating function to prove congruences for the coefficients at(n). 1.
