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A closed form for the block-statistic generating function of the $2\times n$ rectangle: the two-row case of Kahane's conjecture
Kahane (arXiv:2607.11225) proves that for a fence poset $P$ of size $n$, $n!\,Ω(P;t)=\sum_{σ\in S_n} t^{\mathrm{bl}(σ)}$, with $\mathrm{bl}(σ)$ a canonical block count, and conjectures (Conjecture 4.4) that the identity extends to the cell poset of any skew shape, with $\mathrm{bl}$ replaced by a co
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