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
VL - 23
SP - 749
EP - 764
JO - Annals of Combinatorics
JF - Annals of Combinatorics
SN - 0218-0006
IS - 3-4
ER -