### arXiv:1708.09109 [math.CO]AbstractReferencesReviewsResources

#### Hook length property of $d$-complete posets via $q$-integrals

Published 2017-08-30Version 1

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.

**Comments:**40 pages, 28 figures

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