Hook length property of d-complete posets via q-integrals
Abstract.
The hook length formula for d-complete posets states that the P-partition
generating function for them is given by a product in terms of hook lengths.
We give a new proof of the hook length formula using q-integrals. The proof
is done by a case-by-case analysis consisting of two steps. First, we
express the P-partition generating function for each case as a q-integral
and then we evaluate the q-integrals. Several q-integrals are evaluated
using partial fraction expansion identities and others are verified by
computer. This is joint work with Meesue Yoo.