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- W2893876233 endingPage "111778" @default.
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- W2893876233 abstract "We construct a non-commutative, non-cocommutative, graded bialgebra $mathbf{Pi}$ with a basis indexed by the permutations in all finite symmetric groups. Unlike the formally similar Malvenuto-Poirier-Reutenauer Hopf algebra, this bialgebra does not have finite graded dimension. After giving formulas for the product and coproduct, we show that there is a natural morphism from $mathbf{Pi}$ to the algebra of quasi-symmetric functions, under which the image of a permutation is its associated Stanley symmetric function. As an application, we use this morphism to derive some new enumerative identities. We also describe analogues of $mathbf{Pi}$ for the other classical types. In these cases, the relevant objects are module coalgebras rather than bialgebras, but there are again natural morphisms to the quasi-symmetric functions, under which the image of a signed permutation is the corresponding Stanley symmetric function of type B, C, or D." @default.
- W2893876233 created "2018-10-05" @default.
- W2893876233 creator A5066022731 @default.
- W2893876233 date "2020-04-01" @default.
- W2893876233 modified "2023-10-18" @default.
- W2893876233 title "Bialgebras for Stanley symmetric functions" @default.
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- W2893876233 doi "https://doi.org/10.1016/j.disc.2019.111778" @default.
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