William J. Keith

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20232026

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2 papers · 1 filter

math.CO2025

Combinatorial proof of a congruence for partitions into two sizes of part

Eli R. DeWitt, William J. Keith

Previous work showed that, for $ν_{2} (n)$ the number of partitions of $n$ into exactly two part sizes, one has $ν_{2} (16 n + 14) \equiv 0 (mod 4)$ . The earlier proof required the techn…

math.CO2025

Reciprocals of false theta functions

William J. Keith

We investigate reciprocals of false theta functions, producing results such as congruences, simple asymptotic bounds, and combinatorial identities. Of particular interest is a conn…