Abstract
The crank is a partition statistic requested by Dyson in 1944 in order to combinatorially prove a Ramanujan congruence for 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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