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
- Alex Chengyu Li (ORCID: https://orcid.org/0009-0008-4516-8946)
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