Abstract:We give explicit positive combinatorial interpretations for the plethysm coefficients $\langle s_\mu[s_\nu], s_\lambda\rangle$, when $\lambda$ has at most two rows, as counting certain marked trees. In the special case $\mu=(n)$, this also yields a combinatorial interpretation for the corresponding rectangular Kronecker coefficient $g(\lambda, (n^k), (n^k))$. 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.
From: Joshua Swanson [view email]
[v1]
Tue, 4 Nov 2025 06:51:11 UTC (26 KB)
[v2]
Mon, 8 Jun 2026 03:10:32 UTC (35 KB)
[v3]
Mon, 27 Jul 2026 10:03:27 UTC (35 KB)
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