Séminaire Lotharingien de Combinatoire, 85B.85 (2021), 12 pp.
GaYee Park
Naruse Hook Formula for Linear Extensions of Mobile Posets
Abstract.
Linear extensions of posets are important objects in enumerative and algebraic combinatorics that are difficult to count in general. Families of posets like straight shapes and d-complete posets have hook-length product formulas to count linear extensions whereas families like skew shapes have determinant or positive sum formulas like the Naruse hook length formula from 2014. In 2020, Garver et. al. gave determinant formulas to count linear extensions of a family of posets called mobile posets that refine d-complete posets and border strip skew shapes. We give a Naruse type hook length formula to count linear extensions of such posets as well as q-analogues of our formula in both major and inversion index.
Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.
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