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- W3201164877 abstract "The notion of a descent polynomial, a function in enumerative combinatorics that counts permutations with specific properties, enjoys a revived recent research interest due to its connection with other important notions in combinatorics, viz. peak polynomials and symmetric functions. We define the function dm(I,n) as a generalization of the descent polynomial and we prove that for any positive integer m, this function is a polynomial in n for sufficiently large n (similarly to the descent polynomial). We obtain an explicit formula for dm(I,n) when m is sufficiently large. We look at the coefficients of dm(I,n) in different falling factorial bases. We prove the positivity of the coefficients and discover a combinatorial interpretation for them. This result is similar to the positivity result of Diaz-Lopez et al. for the descent polynomial." @default.
- W3201164877 created "2021-09-27" @default.
- W3201164877 creator A5068787816 @default.
- W3201164877 date "2023-01-01" @default.
- W3201164877 modified "2023-09-25" @default.
- W3201164877 title "A generalization of descent polynomials" @default.
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- W3201164877 doi "https://doi.org/10.1016/j.disc.2022.113105" @default.
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