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Discrete Mathematics & Theoretical Computer Science |
Anouk Bergeron-Brlek - Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups
dmtcs:3609 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3609Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral GroupsArticle
- 1 Department of Mathematics and Statistics [Toronto]
We consider the graded Hopf algebra $NCSym$ of symmetric functions with non-commutative variables, which is analogous to the algebra $Sym$ of the ordinary symmetric functions in commutative variables. We give formulaes for the product and coproduct on some of the analogues of the $Sym$ bases and expressions for a shuffle product on $NCSym$. We also consider the invariants of the hyperoctahedral group in the non-commutative case and a state a few results.
Source: HAL:hal-01185143v1
Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: invariants,symmetric function,non-commutative variables,Hopf algebra,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
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