TY - CHAP

T1 - A Lecture Hall Theorem for m-Falling Partitions

AU - Fu, Shishuo

AU - Tang, Dazhao

AU - Yee, Ae Ja

N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-030-57050-7_23

DO - 10.1007/978-3-030-57050-7_23

M3 - Chapter

AN - SCOPUS:85101977096

T3 - Trends in Mathematics

SP - 395

EP - 410

BT - Trends in Mathematics

PB - Springer Science and Business Media Deutschland GmbH

ER -