On the combinatorics of lecture hall partitions

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17 Citations (SciVal)


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.

Original languageEnglish (US)
Pages (from-to)247-262
Number of pages16
JournalRamanujan Journal
Issue number3
StatePublished - Sep 2001

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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