The Refined Lecture Hall Theorem via Abacus Diagrams

2012/11/15 by Laura Bradford, Meredith Harris, Bradford, Laura +9
Mathematics · #05A17 #11P84 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1211.3702

openalex publication_date 2012/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Bousquet-Mélou & Eriksson's lecture hall theorem generalizes Euler's celebrated distinct-odd partition theorem. We present an elementary and transparent proof of a refined version of the lecture hall theorem using a simple bijection involving abacus diagrams.

Related

• Euler's partition theorem and lecture hall partition theorem
• Odd number and Trapezoidal number
• The mathematics of lecture hall partitions
• Lecture Hall Theorems, q-series and Truncated Objects
• The (k,l)-Euler theorem and the combinatorics of (k,l)-sequences