Séminaire Lotharingien de Combinatoire, 80B.28 (2018), 12 pp.
Jang Soo Kim and Meesue Yoo
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
of d-complete posets using q-integrals. Proctor proved that any
connected d-complete poset can be uniquely decomposed into
irreducible d-complete posets and classified all irreducible
d-complete posets. In this work, we prove the hook length property
of all the irreducible d-complete posets.
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.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
The following versions are available: