{"paper":{"title":"A simplicial complex spliting associativity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RA","authors_text":"Daniel L\\'opez, Louis-Fran\\c{c}ois Pr\\'eville-Ratelle, Mar\\'i a Ronco","submitted_at":"2019-06-06T22:12:03Z","abstract_excerpt":"We introduce a simplicial object $(\\{ \\Dy^m\\}_{m\\geq 0}, {\\mathbb F}_i, {\\mathbb S}_j)$ in the category of non-symmetric algebraic operads, satisfying that $\\Dy^0$ is the operad of associative algebras and $\\Dy^1$ is J.-L. Loday\\rq s operad of dendriform algebras. The dimensions of the operad $\\Dy^m$ are given by the Fuss-Catalan numbers.\n  Given a family of partially ordered sets ${\\bold P}=\\{P_n\\}_{n\\geq 1}$ we show that, under certain conditions, the vector space spanned by the set of $m$-simpleces of ${\\bold P}$ is a $\\Dy^m$ algebra. This construction, applied to certain combinatorial Hopf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02834","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"}