Counting linear extensions of posets with determinants of hook lengths

23 Feb 2020 Garver Alexander Grosser Stefan Matherne Jacob P. Morales Alejandro H.

We introduce a class of posets, which includes both ribbon posets (skew shapes) and $d$-complete posets, such that their number of linear extensions is given by a determinant of a matrix whose entries are products of hook lengths. We also give $q$-analogues of this determinantal formula in terms of the major index and inversion statistics... (read more)

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