More shifted partition identities
by
Frank Garvan
University of Florida

Let S, T be sets of positive integers. Let p(S, n) denote the number of partitions of n into elements from the set S. A shifted partition identity takes the form

p(S, n) = p(T, n - 1),       for all n > 0.

Hitherto, there are only a handful of known shifted partition identities. These were discovered by Andrews and Kalvade. We present a host of new shifted partition identities and conjecture that there are infinitely many.

Date received: March 17, 2000