2013/06/30 by Samuele Giraudo
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Associative property #Combinatorial proof #Commutative property #Homotopy and Cohomology in Algebraic Topology #Integer (computer science) #Monoid #Multiplicative function #Quotient #math.CO #math.QA
paper · pdf · doi:10.1007/s10801-014-0543-4
published as Journal of Algebraic Combinatorics, 41, Issue 2, 493--538, 2015 · 42 pages. Complete version of the extended abstracts arXiv:1208.0920 and arXiv:1208.0922
openalex publication_date 2014/08/13 · arxiv created 2015/02/09 · arxiv updated 2015/02/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operads obtained from usual monoids such as the additive and multiplicative monoids of integers and cyclic monoids. They involve various familiar combinatorial objects: endofunctions, parking functions, packed words, permutations, planar rooted trees, trees with a fixed arity, Schröder trees, Motzkin words, integer compositions, directed animals, and segmented integer compositions. We also recover some already known (symmetric or not) operads: the magmatic operad, the associative commutative operad, the diassociative operad, and the triassociative operad. We provide presentations by generators and relations of all constructed nonsymmetric operads.