A Ramanujan congruence analogue for Han's hook-length formula mod 5, and other symmetries

Details A Ramanujan congruence analogue for Han's hook-length formula mod 5, and other symmetries A Ramanujan congruence analogue for Han's hook-length formula mod 5, and other symmetries

2011-09-06

arxiv.org/abs/1109.1236v1

Mathematics

Combinatorics

11 pages; to be presented at Integers Conference 2011

Scientific paper

This article considers the eta power $\prod (1 - q^k)^{b-1}$. It is proved
that the coefficients of $\frac{q^n}{n!}$ in this expression, as polynomials in
b, exhibit equidistribution of the coefficients in the nonzero residue classes
mod 5 when n = 5j + 4. Other symmetries, as well as symmetries for other primes
and prime powers, are proved.

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