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- W4229000623 abstract "We give a combinatorial description for the weak order on the hyperoctahedral group. This characterization is then used to analyze the order-theoretic properties of the shifted products of hyperoctahedral groups. It is shown that each shifted product is a disjoint union of some intervals, which can be convex embedded into a hyperoctahedral group. As an application, we investigate the monomial basis for the Hopf algebra $mathfrak{H}Sym$ of signed permutations, related to the fundamental basis via Mobius inversion on the weak order on hyperoctahedral groups. It turns out that the image of a monomial basis element under the descent map from $mathfrak{H}Sym$ to the algebra of type $B$ quasi-symmetric functions is either zero or a monomial quasi-symmetric function of type $B$." @default.
- W4229000623 created "2022-05-08" @default.
- W4229000623 creator A5087148236 @default.
- W4229000623 date "2022-05-02" @default.
- W4229000623 modified "2023-09-29" @default.
- W4229000623 title "The weak order on the hyperoctahedral group and the monomial basis for the Hopf algebra of signed permutations" @default.
- W4229000623 doi "https://doi.org/10.48550/arxiv.2205.01266" @default.
- W4229000623 hasPublicationYear "2022" @default.
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