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- W4385825616 abstract "PED partitions are partitions with even parts distinct while odd parts are unrestricted. Similarly, POD partitions have distinct odd parts while even parts are unrestricted. Merca proved several recurrence relations analytically for the number of PED partitions of $n$. They are similar to the recurrence relation for the number of partitions of $n$ given by Euler's pentagonal number theorem. We provide combinatorial proofs for all of these theorems and also for the pentagonal number theorem for PED partitions proved analytically by Fink, Guy, and Krusemeyer. Moreover, we prove combinatorially a recurrence for POD partitions given by Ballantine and Merca, Beck-type identities involving PED and POD partitions, and several other results about PED and POD partitions." @default.
- W4385825616 created "2023-08-15" @default.
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- W4385825616 date "2023-08-11" @default.
- W4385825616 modified "2023-09-26" @default.
- W4385825616 title "PED and POD partitions: combinatorial proofs of recurrence relations" @default.
- W4385825616 doi "https://doi.org/10.48550/arxiv.2308.06123" @default.
- W4385825616 hasPublicationYear "2023" @default.
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