Geodesic
Naruse hook formula for linear extensions of mobile posets
GaYee Park1
1University of Massachusetts Amherst
The electronic journal of combinatorics, Tome 29 (2022) no. 3
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Linear extensions of posets are important objects in enumerative and algebraic combinatorics that are difficult to count in general. Families of posets like Young diagrams of straight shapes and d-complete posets have hook length product formulas to count linear extensions, whereas families like Young diagrams of 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 by proving a major index q-analogue. We also a inversion index q-analogue of the Naruse formula for mobile tree posets.
DOI : 10.37236/10444
Classification : 05A15, 05A05, 06A07, 14N15
Mots-clés : posets, descents, linear extensions, determinants, hook lengths

GaYee Park  1

1 University of Massachusetts Amherst 
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     journal = {The electronic journal of combinatorics},
     year = {2022},
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     number = {3},
     doi = {10.37236/10444},
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GaYee Park. Naruse hook formula for linear extensions of mobile posets. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10444

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