Combinatorial operads from monoids View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-03

AUTHORS

Samuele Giraudo

ABSTRACT

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. More... »

PAGES

493-538

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10801-014-0543-4

DOI

http://dx.doi.org/10.1007/s10801-014-0543-4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1051333474


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