TY - JOUR

T1 - A Lecture Hall Theorem for m -Falling Partitions

AU - Fu, Shishuo

AU - Tang, Dazhao

AU - Yee, Ae Ja

N1 - Funding Information:
This collaboration was initiated at the Pennsylvania State University in the summer of 2018, and we would like to thank the Department of Mathematics for hospitality. The authors are indebted to the anonymous referee for his/her helpful comments and suggestions.

PY - 2019/11/1

Y1 - 2019/11/1

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/s00026-019-00452-9

DO - 10.1007/s00026-019-00452-9

M3 - Article

AN - SCOPUS:85074721637

SN - 0218-0006

VL - 23

SP - 749

EP - 764

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 3-4

ER -