A combinatorial interpretation for certain plethysm and Kronecker coefficients
Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Pak, Igor, Panova, Greta, Swanson, Joshua P.
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7103983693
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