arXiv 1306.69382013-06math.COmath.QA

Combinatorial operads from monoids

Samuele Giraudo

备注：: 42 pages. Complete version of the extended abstracts arXiv:1208.0920 and arXiv:1208.0922
发表信息：: Journal of Algebraic Combinatorics, 41, Issue 2, 493--538, 2015
DOI：: 10.1007/s10801-014-0543-4

英文摘要：

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.

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