Séminaire Lotharingien de Combinatoire, 85B.60 (2021), 12 pp.
Alexander Garver, Stefan Grosser, Jacob P. Matherne and Alejandro H. Morales
Counting Linear Extensions of Posets with Determinants of Hook Lengths
Abstract.
We introduce a class of posets, called mobile posets, which includes both ribbon posets and d-complete posets, whose number of linear extensions is given by a determinant of a matrix where entries are products of hook lengths. We also give q-analogs of this determinantal formula in terms of the inversion statistic.
Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.
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