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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.00574 |
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| _version_ | 1866916491339759616 |
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| author | Arcis, Diego González, Camilo Márquez, Sebastián |
| author_facet | Arcis, Diego González, Camilo Márquez, Sebastián |
| contents | In 2004, Rosas and Sagan developed the theory of symmetric functions in noncommuting variables, achieving results analogous to classical symmetric functions. On the other hand, in 2004, Desrosiers, Lapointe and Mathieu introduced the theory of symmetric functions in superspace, which involve both commuting and anticommuting variables, extending the classic theory. Here, we introduce symmetric functions in noncommuting variables in superspace. We define the classical symmetric functions in noncommuting variables to superspace: monomials, power sums, elementaries and complete homogeneous, which generalize both the ones studied by Rosas and Sagan and the ones studied by Desrosiers, Lapointe and Mathieu. We also define Schur--type functions in noncommuting variables in superspace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00574 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetric functions in noncommuting variables in superspace Arcis, Diego González, Camilo Márquez, Sebastián Combinatorics 05E05 In 2004, Rosas and Sagan developed the theory of symmetric functions in noncommuting variables, achieving results analogous to classical symmetric functions. On the other hand, in 2004, Desrosiers, Lapointe and Mathieu introduced the theory of symmetric functions in superspace, which involve both commuting and anticommuting variables, extending the classic theory. Here, we introduce symmetric functions in noncommuting variables in superspace. We define the classical symmetric functions in noncommuting variables to superspace: monomials, power sums, elementaries and complete homogeneous, which generalize both the ones studied by Rosas and Sagan and the ones studied by Desrosiers, Lapointe and Mathieu. We also define Schur--type functions in noncommuting variables in superspace. |
| title | Symmetric functions in noncommuting variables in superspace |
| topic | Combinatorics 05E05 |
| url | https://arxiv.org/abs/2312.00574 |