Exact Enumeration and Fixed-Rank Asymptotics of Ballot-Admissible Fibonacci Ribbons

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-26
DOI
https://doi.org/10.5281/zenodo.22104113
Primary Topic
Advanced Combinatorial Mathematics
Type
preprint
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preprint

Exact Enumeration and Fixed-Rank Asymptotics of Ballot-Admissible Fibonacci Ribbons

Alex Chengyu Li
Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
preprint

Exact Enumeration and Fixed-Rank Asymptotics of Ballot-Admissible Fibonacci Ribbons

Alex Chengyu Li
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
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Exact Enumeration and Fixed-Rank Asymptotics of Ballot-Admissible Fibonacci Ribbons — Alex Chengyu Li · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS