{"paper":{"title":"Intervals in a family of Fibonacci lattices","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jean-Luc Baril, Nathana\\\"el Hassler","submitted_at":"2024-11-26T17:40:09Z","abstract_excerpt":"We focus on a family of subsets $(\\F^p_n)_{p\\geq 2}$ of Dyck paths of semilength $n$ that avoid the patterns $DUU$ and $D^{p+1}$, which are enumerated by the generalized Fibonacci numbers. We endow them with the partial order relation induced by the well-known Stanley lattice, and we prove that all these posets are sublattices of the Stanley lattice. We provide generating functions for the numbers of linear and boolean intervals and we deduce the M\\\"obius function for every $p\\geq 2$. We count meet-irreducible elements in $\\FF_n^p$ which establishes a surprising link with the edges of the $(n,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17628","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/2411.17628/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"}