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 the others are verified by computer.