2022/03/03 by Cristina Ballantine, Ballantine, Cristina, Mircea Merca +1
Mathematics · #05A19 #05A20 #11P81 #11P82 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2203.02061
openalex publication_date 2022/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.