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Combinatorial analysis reveals exact enumeration formulas and fixed-rank asymptotics for ballot-admissible Fibonacci ribbons, proving the 1/e limiting-proportion conjecture.
Tenn asked for the enumeration of ballot-admissible Fibonacci ribbon tableaux beyond the three-letter case. This paper gives an exact finite formula for every alphabet size by encoding ribbon columns as an alternating defining/dual dominant walk and contracting the unique ballot-neutral forbidden adjacency. The construction also gives a highest-weight refinement in Schur coefficients, an exact generating-function substitution, explicit fixed-rank leading asymptotics, a stable interpretation by involutions without adjacent transpositions, a Poisson limit proving the recorded 1/e limiting-proportion conjecture, and polynomial near-stable defects on every fixed-distance line n=k-r. Formalization status: a Lean 4 formalization of the finite combinatorial identities is in progress.
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Alex Chengyu Li (2026) studied this question.
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