Lecture Hall Partitions

Phil Busse

Friday, March 12, 2004
1:00 pm, 845 Patterson Office Tower

Abstract:

Lecture hall partitions are a subclass of integer partitions with n parts. They are so-named because they describe all ways of designing a lecture hall with n rows of integer heights such that each row has a clear view of the speaker. Mireille Bousquet-Mélou and Kimmo Eriksson showed the number of lecture hall partitions of length n has the same generating function as the number of integer partitions having distinct parts with at most n parts. This result is a finite version of Euler's result that the number of integer partitions using odd parts is equinumerous with the number of integer partions using distinct parts. At the end, I will briefly discuss the application of the Lecture Hall Theorem in proving Bott's formula for the Poincaré series of C_n and \tilde{C_n}, the affine Weyl group of type C.