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- W4300979405 abstract "Noticing that some recent variations of descent polynomials are special cases of Carlitz and Scoville's four-variable polynomials, which enumerate permutations by the parity of descent and ascent positions, we prove a $q$-analogue of Carlitz-Scoville's generating function by counting the inversion number and a type B analogue by enumerating the signed permutations with respect to the parity of desecnt and ascent positions. As a by-product of our formulas, we obtain a $q$-analogue of Chebikin's formula for alternating descent polynomials, an alternative proof of Sun's gamma-positivity of her bivariate Eulerian polynomials and a type B analogue, the latter refines Petersen's gamma-positivity of the type B Eulerian polynomials." @default.
- W4300979405 created "2022-10-04" @default.
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- W4300979405 date "2022-09-30" @default.
- W4300979405 modified "2023-10-16" @default.
- W4300979405 title "Enumeration of permutations by the parity of descent positions" @default.
- W4300979405 doi "https://doi.org/10.48550/arxiv.2209.15302" @default.
- W4300979405 hasPublicationYear "2022" @default.
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