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Extensions And Bijections Of Skew-Shaped Tableaux And Factorizations Of Singer Cycles, Ga Yee Park

Doctoral Dissertations

This dissertation is in the field of Algebraic and Enumerative Combinatorics. In the first part of the thesis, we study the generalization of Naruse hook-length formula to mobile posets. 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 (NHLF). 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 …