### Abstract

For an integer m≥ 2 , a partition λ= (λ_{1}, λ_{2}, …) is called m-falling, a notion introduced by Keith, if the least non-negative residues mod m of λ_{i}’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

*Annals of Combinatorics*,

*23*(3-4), 749-764. https://doi.org/10.1007/s00026-019-00452-9

}

*Annals of Combinatorics*, vol. 23, no. 3-4, pp. 749-764. https://doi.org/10.1007/s00026-019-00452-9

**A Lecture Hall Theorem for m -Falling Partitions.** / Fu, Shishuo; Tang, Dazhao; Yee, Ae Ja.

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 -