.
We give two proofs: one via Bott's formula for the Poincaré series of
the affine Coxeter group 
, and one direct proof.
MIREILLE BOUSQUET-MELOU
LaBRI,
Université Bordeaux 1,
351 cours de la Libération,
33 405 Talence Cedex, France
bousquet@labri.u-bordeaux.fr
KIMMO ERIKSSON
Department of Mathematics,
Stockholm University,
S-106 91 Stockholm, Sweden
kimmo@nada.kth.se
Received February 21, 1996; Accepted February 22, 1996
Abstract.
We prove a finite version of the well-known theorem that says that the
number of partitions of an integer N into distinct parts is equal
to the number of partitions of N into odd parts. Our version says that
the number of ``lecture hall partitions of length
n'' of N equals the
number of partitions of N into small odd parts: .
We give two proofs: one via Bott's formula for the Poincaré series of
the affine Coxeter group , and one direct proof.
Keywords: integer partitions, affine Coxeter groups
1991 Mathematics Classification: Primary - 05A17, 05E15