Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups
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 exp...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2008-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/3609/pdf |
| _version_ | 1797270405593956352 |
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| author | Anouk Bergeron-Brlek |
| author_facet | Anouk Bergeron-Brlek |
| author_sort | Anouk Bergeron-Brlek |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:03:45Z |
| format | Article |
| id | doaj.art-2b98ac1137604be9852dff61fcbc70d7 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:45Z |
| publishDate | 2008-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-2b98ac1137604be9852dff61fcbc70d72024-03-07T14:38:06ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502008-01-01DMTCS Proceedings vol. AJ,...Proceedings10.46298/dmtcs.36093609Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral GroupsAnouk Bergeron-Brlek0Department 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.https://dmtcs.episciences.org/3609/pdfinvariantssymmetric functionnon-commutative variableshopf algebra[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Anouk Bergeron-Brlek Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups Discrete Mathematics & Theoretical Computer Science 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] |
| title | Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups |
| title_full | Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups |
| title_fullStr | Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups |
| title_full_unstemmed | Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups |
| title_short | Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups |
| title_sort | invariants in non commutative variables of the symmetric and hyperoctahedral groups |
| topic | 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] |
| url | https://dmtcs.episciences.org/3609/pdf |
| work_keys_str_mv | AT anoukbergeronbrlek invariantsinnoncommutativevariablesofthesymmetricandhyperoctahedralgroups |