{"paper":{"title":"Algebraic structures defined on $m$-Dyck paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CO","authors_text":"Daniel L\\'opez N., Louis-Fran\\c{c}ois Pr\\'eville-Ratelle, Mar\\'ia Ronco","submitted_at":"2015-08-06T00:48:11Z","abstract_excerpt":"We introduce natural binary set-theoretical products on the set of all $m$-Dyck paths, which led us to define a non-symmetric algebraic operad $\\Dy^m$, described on the vector space spanned by $m$-Dyck paths. Our construction is closely related to the $m$-Tamari lattice, so the products defining $\\Dy^m$ are given by intervals in this lattice. For $m=1$, we recover the notion of dendriform algebra introduced by J.-L. Loday in \\cite{Lod}, and there exists a natural operad morphism from the operad ${\\mbox {\\it Ass}}$ of associative algebras into the operad $\\Dy^m$, consequently $\\Dy ^m$ is a Hopf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01252","kind":"arxiv","version":2},"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"}