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Dyson's crank and unimodal compositions
Published 3 Mar 2022 in math.CO and math.NT | (2203.02061v1)
Abstract: The crank is a partition statistic requested by Dyson in 1944 in order to combinatorially prove a Ramanujan congruence of Euler's partition function $p(n)$. In this paper, we provide connections between Dyson's crank and unimodal compositions. Somewhat unrelated, we give a combinatorial proof of a new truncated Euler pentagonal number theorem due to Xia and Zhao.
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