William Keith

$William Keith$

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Recent Publications

Congruences for 9-regular partitions modulo 3. Ramanujan Journal. Read More
A Ramanujan congruence analogue for Han's hook-length formula mod 5, and other symmetries. Acta Arithmetica. Read More
(Joint w/Robert Boyer) Stabilization of coefficients for partition polynomials. Integers. Read More

Research Projects

2-arity and 3-arity for regular partitions. There are no arithmetic progressions An+B in which the partition numbers p(An+B) are all even or odd, and there are almost certainly none which have a constant residue modulo 3. Yet many such progressions exist for the m-regular partitions for many m. I am interested in why this is the case and how we might be able to prove general theorems about such progressions in large families. Perhaps the investigation will shed light on the parity and 3-arity of the usual partition function.

Teaching Experience