Congruences for Han’s Generating Function
نویسندگان
چکیده
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).
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