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A Refinement of the Lecture Hall Theorem

✍ Scribed by Mireille Bousquet-Mélou; Kimmo Eriksson

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
225 KB
Volume
86
Category
Article
ISSN
0097-3165

No coin nor oath required. For personal study only.

✦ Synopsis

For n 1, let L n be the set of lecture hall partitions of length n, that is, the set of n-tuples of integers *=(* 1 , ..., * n ) satisfying 0 * 1 Â1 * 2 Â2 } } } * n Ân. Let W*X be the partition (W* 1 Â1X, ..., W* n ÂnX), and let o(W*X) denote the number of its odd parts. We show that the identity :

is equivalent to a refinement of Bott's formula for the affine Coxeter group C n , obtained by I. G. Macdonald (Math. Ann. 199 (1972), 161 174) and V. Reiner (Electron. J. Combin. 2 (1995), R25). The case u=v=1 of the above identity, called the lecture hall theorem, was proved by us in (

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