### Abstract

A lecture hall partition of length n is an integer sequence λ = (λ_{1},..., λ_{n}) satisfying 0 ≤ λ_{1}/1 ≤ λ_{2}/2 ≤ ... ≤ λ_{n}/n. (1) Bousquet-Mélou and Eriksson showed that the number of lecture hall partitions of length n of a positive integer N whose alternating sum is k equals the number of partitions of N into k odd parts less than 2n. We prove the fact by a natural combinatorial bijection. This bijection, though defined differently, is essentially the same as one of the bijections found by Bousquet-Mélou and Eriksson.

Original language | English (US) |
---|---|

Pages (from-to) | 247-262 |

Number of pages | 16 |

Journal | Ramanujan Journal |

Volume | 5 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 2001 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

}

*Ramanujan Journal*, vol. 5, no. 3, pp. 247-262. https://doi.org/10.1023/A:1012918510262

**On the combinatorics of lecture hall partitions.** / Yee, Ae Ja.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the combinatorics of lecture hall partitions

AU - Yee, Ae Ja

PY - 2001/9/1

Y1 - 2001/9/1

N2 - A lecture hall partition of length n is an integer sequence λ = (λ1,..., λn) satisfying 0 ≤ λ1/1 ≤ λ2/2 ≤ ... ≤ λn/n. (1) Bousquet-Mélou and Eriksson showed that the number of lecture hall partitions of length n of a positive integer N whose alternating sum is k equals the number of partitions of N into k odd parts less than 2n. We prove the fact by a natural combinatorial bijection. This bijection, though defined differently, is essentially the same as one of the bijections found by Bousquet-Mélou and Eriksson.

AB - A lecture hall partition of length n is an integer sequence λ = (λ1,..., λn) satisfying 0 ≤ λ1/1 ≤ λ2/2 ≤ ... ≤ λn/n. (1) Bousquet-Mélou and Eriksson showed that the number of lecture hall partitions of length n of a positive integer N whose alternating sum is k equals the number of partitions of N into k odd parts less than 2n. We prove the fact by a natural combinatorial bijection. This bijection, though defined differently, is essentially the same as one of the bijections found by Bousquet-Mélou and Eriksson.

UR - http://www.scopus.com/inward/record.url?scp=0035729473&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035729473&partnerID=8YFLogxK

U2 - 10.1023/A:1012918510262

DO - 10.1023/A:1012918510262

M3 - Article

AN - SCOPUS:0035729473

VL - 5

SP - 247

EP - 262

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

IS - 3

ER -