A Lecture Hall Theorem for m-Falling Partitions

Shishuo Fu, Dazhao Tang, Ae Ja Yee

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

For an integer m ≥ 2, a partition λ = (λ1, λ2,..) is called m-falling, a notion introduced by Keith, if the least non-negative residues mod m of λi’s form a nonincreasing sequence. We extend a bijection originally due to the third author to deduce a lecture hall theorem for such m-falling partitions. A special case of this result gives rise to a finite version of Pak–Postnikov’s (m, c)-generalization of Euler’s theorem. Our work is partially motivated by a recent extension of Euler’s theorem for all moduli, due to Xiong and Keith. We note that their result actually can be refined with one more parameter.

Original languageEnglish (US)
Title of host publicationTrends in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Pages395-410
Number of pages16
DOIs
StatePublished - 2021

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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