A New Symmetric Function Identity With an Application to symmetric group character values
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929530013220864 |
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| author | Westrem, Karlee J. |
| author_facet | Westrem, Karlee J. |
| contents | Symmetric functions show up in several areas of mathematics including enumerative combinatorics and representation theory. Tewodros Amdeberhan conjectures equalities of $Σ_n$ characters sums over a new set called $Ev(λ)$. When investigating the alternating sum of characters for $Ev(λ)$ written in terms of the inner product of Schur functions and power sum symmetric functions, we found an equality between the alternating sum of power sum symmetric polynomials and a product of monomial symmetric polynomials. As a consequence, a special case of an alternating sum of $Σ_n$ characters over the set $Ev(λ)$ equals $0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04644 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A New Symmetric Function Identity With an Application to symmetric group character values Westrem, Karlee J. Combinatorics Representation Theory Symmetric functions show up in several areas of mathematics including enumerative combinatorics and representation theory. Tewodros Amdeberhan conjectures equalities of $Σ_n$ characters sums over a new set called $Ev(λ)$. When investigating the alternating sum of characters for $Ev(λ)$ written in terms of the inner product of Schur functions and power sum symmetric functions, we found an equality between the alternating sum of power sum symmetric polynomials and a product of monomial symmetric polynomials. As a consequence, a special case of an alternating sum of $Σ_n$ characters over the set $Ev(λ)$ equals $0$. |
| title | A New Symmetric Function Identity With an Application to symmetric group character values |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2410.04644 |