Combinatorial operads from monoids

Combinatorial operads from monoids

We introduce a functorial construction which, from a monoid, produces a setoperad. 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 r...

Constructing combinatorial operads from monoids

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 operad obtained from the additive monoid. These involve various familiar combinatorial objects: parking functions, packed words, planar rooted trees, generalized Dyck paths, Schröder trees, Motzkin paths, integer compositions, directed an...

Colored operads, series on colored operads, and combinatorial generating systems

A new sort of combinatorial generating system, called bud generating system, is introduced. Bud generating systems are devices for specifying sets of various kinds of combinatorial objects, called languages. They can emulate context-free grammars, regular tree grammars, and synchronous grammars, allowing to work with all these generating systems in a unified way. The theory of bud generating sy...

Combinatorial N-fold Monoidal Categories and N-fold Operads

Operads were originally defined as V-operads, that is, enriched in a symmetric or braided monoidal category V. The symmetry or braiding in V is required in order to describe the associativity axiom the operads must obey, as well as the associativity that must be a property of the action of an operad on any of its algebras. A sequence of categorical types that filter the category of monoidal cat...

Combinatorial Group Theory, Inverse Monoids, Automata, And Global Semigroup Theory