Decomposition of Polysymmetric Functions and Stack Partitions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909988259102720 |
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| author | Martinez, David |
| author_facet | Martinez, David |
| contents | Polysymmetric functions, introduced by Asvin G and Andrew O'Desky as a generalization of symmetric functions, have natural connections to algebraic geometry and provide a foundation for further developments. In this paper, we study polysymmetric functions using stack partitions and develop combinatorial descriptions of several polysymmetric bases. We introduce two new signed polysymmetric bases and give explicit transition formulas among the monomial, homogeneous, elementary, power, and signed polysymmetric bases. These results extend many familiar identities from symmetric function theory to the polysymmetric setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10377 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decomposition of Polysymmetric Functions and Stack Partitions Martinez, David Combinatorics Algebraic Geometry Primary 05E05, Secondary 05A17 Polysymmetric functions, introduced by Asvin G and Andrew O'Desky as a generalization of symmetric functions, have natural connections to algebraic geometry and provide a foundation for further developments. In this paper, we study polysymmetric functions using stack partitions and develop combinatorial descriptions of several polysymmetric bases. We introduce two new signed polysymmetric bases and give explicit transition formulas among the monomial, homogeneous, elementary, power, and signed polysymmetric bases. These results extend many familiar identities from symmetric function theory to the polysymmetric setting. |
| title | Decomposition of Polysymmetric Functions and Stack Partitions |
| topic | Combinatorics Algebraic Geometry Primary 05E05, Secondary 05A17 |
| url | https://arxiv.org/abs/2510.10377 |