Algebra, Geometry & Combinatorics: Naruse hook formula for linear extensions of mobile posets
- Event Type
- Seminar/Symposium
- Sponsor
- n/a
- Location
- 347 Altgeld Hall
- Date
- Oct 28, 2021 3:00 - 4:00 pm
- Speaker
- GaYee Park
- Contact
- Colleen Robichaux
- cer2@illinois.edu
- Views
- 31
Abstract: Linear extensions of posets are important objects in enumerativevand 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 give an inversion index $q$-analogue of the Naruse formula for mobile tree posets.