{"paper":{"title":"Conway-Coxeter friezes and beyond: Polynomially weighted walks around dissected polygons and generalized frieze patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CO","authors_text":"Christine Bessenrodt","submitted_at":"2014-12-04T16:49:14Z","abstract_excerpt":"Conway and Coxeter introduced frieze patterns in 1973 and classified them via triangulated polygons. The determinant of the matrix associated to a frieze table was computed explicitly by Broline, Crowe and Isaacs in 1974, a result generalized 2012 by Baur and Marsh in the context of cluster algebras of type A. Higher angulations of polygons and associated generalized frieze patterns were studied in a joint paper with Holm and J\\o rgensen. Here we take these results further; we allow arbitrary dissections and introduce polynomially weighted walks around such dissected polygons. The correspondin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1726","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":""},"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"}