Hook Lengths and 3-cores
نویسندگان
چکیده
Recently, the first author generalized a formula of Nekrasov and Okounkov which gives a combinatorial formula, in terms of hook lengths of partitions, for the coefficients of certain power series. In the course of this investigation, he conjectured that a(n) = 0 if and only if b(n) = 0, where integers a(n) and b(n) are defined by
منابع مشابه
Some Conjectures and Open Problems on Partition Hook Lengths
Abstract. We present some conjectures and open problems on partition hook lengths, which are all motivated by known results on the subject. The conjectures are suggested by extensive experimental calculations using a computer algebra system. The first conjecture unifies two classical results on the number of standard Young tableaux and the number of pairs of standard Young tableaux of the same ...
متن کاملm at h . N T ] 1 6 M ay 2 00 8 HOOK LENGTHS AND 3 - CORES
Recently, the first author generalized a formula of Nekrasov and Okounkov which gives a combinatorial formula, in terms of hook lengths of partitions, for the coefficients of certain power series. In the course of this investigation, he conjectured that a(n) = 0 if and only if b(n) = 0, where integers a(n) and b(n) are defined by
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