{"paper":{"title":"Finite-state enumeration of adjacency-constrained 132-avoiding permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dai Akita, Teruki Mayama","submitted_at":"2026-05-22T11:34:27Z","abstract_excerpt":"For a fixed integer $m\\ge 1$, let $\\mathcal{A}_n^{(m)}$ be the set of permutations $\\pi\\in S_n$ that avoid the pattern $132$ and satisfy the adjacency bound $|\\pi_{i+1}-\\pi_i|\\le m$ for all $i$. Here, a pattern $132$ means three indices $i<j<k$ such that $\\pi_i<\\pi_k<\\pi_j$. A recent study initiated the enumeration of these constrained 132-avoiding permutations, treating the case $m=2$ by deriving a rational ordinary generating function and asking for finite-state decompositions, rational generating functions, and explicit rational formulas for larger fixed $m$. We introduce a two-sided endpoi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23519","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.23519/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}