投票条件を満たす Fibonacci リボン表:任意のアルファベット数での完全計数と固定ランク漸近
Ballot-Admissible Fibonacci Ribbon Tableaux: Complete Enumeration for Arbitrary Alphabet Size and Fixed-Rank Asymptotics
研究概要
任意のアルファベット数での数え上げ、最高ウェイトによる精密化、固定ランクでの漸近を与える。
原文要旨(英語)
Tenn proved the three-letter case and left the enumeration of ballot-admissible Fibonacci ribbon tableaux for alphabet sizes n >= 4 open. This work resolves that problem uniformly for every alphabet size n >= 2. Encoding ribbon columns as an alternating dominant type-A walk and contracting the unique ballot-neutral forbidden adjacency yields an exact finite formula and a highest-weight refinement in explicit Schur coefficients.
Exact Weyl integral representations and Regev's strip asymptotics give the fixed-rank leading asymptotic, including an explicit positive constant, for every fixed n >= 3. In the stable range n >= k, the count is the number of involutions with no adjacent transposition; a Poisson limit proves the 1/e limiting-proportion conjecture recorded in OEIS A170941. On each fixed-distance line n = k-r, the defect is eventually polynomial in k.
The accompanying Lean 4 development provides premise-free publication endpoints for all 47 numbered mathematical labels. The complete publication root is checked with --trust=0. Public source and release assets are available at https://github.com/crabsatellite/fibonacci-ribbon-ballot-enumeration.
数学の検証
主要結論には公開されたカーネル検証済みの証明があり、論文との対応も確認されています。これは外部査読とは別の検証です。
検証基準