{"paper":{"title":"A Graded M\\\"obius transform and its harmonic interpretation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Samy Abbes","submitted_at":"2015-05-04T08:09:25Z","abstract_excerpt":"We give a graded version of the M\\\"obius inversion formula in the framework of trace monoids. The formula is based on a graded version of the M\\\"obius transform, related to the notion of height deriving from the Cartier-Foata normal form of the elements of a trace monoid.\n  Using the notion of Bernoulli measures on the boundary of a trace monoid developped recently, we study a probabilistic interpretation of the graded inversion formula. We introduce M\\\"obius harmonic functions for trace monoids and obtain an integral representation formula for them, analogous to the Poisson formula for harmon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00546","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"}