A Lecture Hall Theorem for m -Falling Partitions

Shishuo Fu, Dazhao Tang, Ae Ja Yee

Research output: Contribution to journalArticlepeer-review

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)
Pages (from-to)749-764
Number of pages16
JournalAnnals of Combinatorics
Volume23
Issue number3-4
DOIs
StatePublished - Nov 1 2019

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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