### 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

arXiv:math/0511055 [math.CO] (Published 2005-11-02)

Hook length polynomials for plane forests of a certain type

arXiv:1504.01007 [math.CO] (Published 2015-04-04)

Polynomial Approach to Explicit Formulae for Generalized Binomial Coefficients

arXiv:1708.02995 [math.CO] (Published 2017-08-09)

Loop-augmented forests and a variant of the Foulkes' conjecture