A combinatorial interpretation for certain plethysm and Kronecker coefficients
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909886038671360 |
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| author | Pak, Igor Panova, Greta Swanson, Joshua P. |
| author_facet | Pak, Igor Panova, Greta Swanson, Joshua P. |
| contents | We give explicit positive combinatorial interpretations for the plethysm coefficients $\langle s_μ[s_ν], s_λ\rangle$, when $λ$ has at most two rows, as counting certain marked trees. In the special case $μ=(n)$, this also yields a combinatorial interpretation for the corresponding rectangular Kronecker coefficient $g(λ, (n^k), (n^k))$. While it is easy to express these quantities as differences of counting problems in the complexity class $\mathrm{FP}$, putting the problem in $\#\mathrm{P}$, our interpretations give a positive counting formula over explicit marked trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02312 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A combinatorial interpretation for certain plethysm and Kronecker coefficients Pak, Igor Panova, Greta Swanson, Joshua P. Combinatorics 05A17, 05E05 We give explicit positive combinatorial interpretations for the plethysm coefficients $\langle s_μ[s_ν], s_λ\rangle$, when $λ$ has at most two rows, as counting certain marked trees. In the special case $μ=(n)$, this also yields a combinatorial interpretation for the corresponding rectangular Kronecker coefficient $g(λ, (n^k), (n^k))$. While it is easy to express these quantities as differences of counting problems in the complexity class $\mathrm{FP}$, putting the problem in $\#\mathrm{P}$, our interpretations give a positive counting formula over explicit marked trees. |
| title | A combinatorial interpretation for certain plethysm and Kronecker coefficients |
| topic | Combinatorics 05A17, 05E05 |
| url | https://arxiv.org/abs/2511.02312 |