Seaweed Algebras and the Index Statistic for Partitions

2021/12/17 by Craig, William
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2112.09269

Abstract

In 2018 Coll, Mayers, and Mayers conjectured that the q-series ( q, -q³; q⁴ )_∞^-1 is the generating function for a certain parity statistic related to the index of seaweed algebras. We prove this conjecture. Thanks to earlier work by Seo and Yee, the conjecture would follow from the non-negativity of the coefficients of this infinite product. Using a variant of the circle method along with Euler-Maclaurin summation, we establish this non-negativity, thereby confirming the Coll-Mayers-Mayers Conjecture.

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