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 language | English (US) |
|---|---|
| Pages (from-to) | 749-764 |
| Number of pages | 16 |
| Journal | Annals of Combinatorics |
| Volume | 23 |
| Issue number | 3-4 |
| DOIs | |
| State | Published - Nov 1 2019 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
Cite this
}
A Lecture Hall Theorem for m -Falling Partitions. / Fu, Shishuo; Tang, Dazhao; Yee, Ae Ja.
In: Annals of Combinatorics, Vol. 23, No. 3-4, 01.11.2019, p. 749-764.Research output: Contribution to journal › Article
TY - JOUR
T1 - A Lecture Hall Theorem for m -Falling Partitions
AU - Fu, Shishuo
AU - Tang, Dazhao
AU - Yee, Ae Ja
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.
UR - http://www.scopus.com/inward/record.url?scp=85074721637&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85074721637&partnerID=8YFLogxK
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 -