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- W4386501276 abstract "We construct a new family $left( eta_{alpha}^{left( qright) }right) _{alphainoperatorname*{Comp}}$ of quasisymmetric functions for each element $q$ of the base ring. We call them the enriched $q$-monomial quasisymmetric functions. When $r:=q+1$ is invertible, this family is a basis of $operatorname{QSym}$. It generalizes Hoffman's essential quasi-symmetric functions (obtained for $q=0$) and Hsiao's monomial peak functions (obtained for $q=1$), but also includes the monomial quasisymmetric functions as a limiting case. We describe these functions $eta_{alpha}^{left( qright) }$ by several formulas, and compute their products, coproducts and antipodes. The product expansion is given by an exotic variant of the shuffle product which we call the stufufuffle product due to its ability to pick several consecutive entries from each composition. This stufufuffle product has previously appeared in recent work by Bouillot, Novelli and Thibon, generalizing the block shuffle product from the theory of multizeta values." @default.
- W4386501276 created "2023-09-08" @default.
- W4386501276 creator A5007117776 @default.
- W4386501276 creator A5074897310 @default.
- W4386501276 date "2023-09-03" @default.
- W4386501276 modified "2023-09-27" @default.
- W4386501276 title "The enriched $q$-monomial basis of the quasisymmetric functions" @default.
- W4386501276 doi "https://doi.org/10.48550/arxiv.2309.01118" @default.
- W4386501276 hasPublicationYear "2023" @default.
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