On q-series identities arising from lecture hall partitions

George E. Andrews; Sylvie Corteel; Carla D. Savage

doi:10.1142/S1793042109002134

On q-series identities arising from lecture hall partitions

George E. Andrews
, Sylvie Corteel
, Carla D. Savage

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, we highlight two q-series identities arising from the "five guidelines" approach to enumerating lecture hall partitions and give direct, q-series proofs. This requires two new finite corollaries of a q-analog of Gauss's second theorem. In fact, the method reveals stronger results about lecture hall partitions and anti-lecture hall compositions that are only partially explained combinatorially.

Original language	English (US)
Pages (from-to)	327-337
Number of pages	11
Journal	International Journal of Number Theory
Volume	5
Issue number	2
DOIs	https://doi.org/10.1142/S1793042109002134
State	Published - 2009

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1142/S1793042109002134

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author = "Andrews, \{George E.\} and Sylvie Corteel and Savage, \{Carla D.\}",

note = "Funding Information: The first-named author{\textquoteright}s research was partially supported by the NSF grant DMS-0200047. The third-named author{\textquoteright}s research was partially supported by the NSF grants DMS-0300034 and INT-0230800.",

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AU - Andrews, George E.

AU - Corteel, Sylvie

AU - Savage, Carla D.

N1 - Funding Information: The first-named author’s research was partially supported by the NSF grant DMS-0200047. The third-named author’s research was partially supported by the NSF grants DMS-0300034 and INT-0230800.

PY - 2009

Y1 - 2009

N2 - In this paper, we highlight two q-series identities arising from the "five guidelines" approach to enumerating lecture hall partitions and give direct, q-series proofs. This requires two new finite corollaries of a q-analog of Gauss's second theorem. In fact, the method reveals stronger results about lecture hall partitions and anti-lecture hall compositions that are only partially explained combinatorially.

AB - In this paper, we highlight two q-series identities arising from the "five guidelines" approach to enumerating lecture hall partitions and give direct, q-series proofs. This requires two new finite corollaries of a q-analog of Gauss's second theorem. In fact, the method reveals stronger results about lecture hall partitions and anti-lecture hall compositions that are only partially explained combinatorially.

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UR - https://www.scopus.com/pages/publications/65449143911#tab=citedBy

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DO - 10.1142/S1793042109002134

M3 - Article

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SP - 327

EP - 337

JO - International Journal of Number Theory

JF - International Journal of Number Theory

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ER -

On q-series identities arising from lecture hall partitions

Abstract

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