60 citations · 179 across the 42 of their papers we have counts for
5 papers · 1 filter
Cliff operads: a hierarchy of operads on words
Camille Combe, Samuele Giraudo
A new hierarchy of operads over the linear spans of -cliffs, which are some words of integers, is introduced. These operads are intended to be analogues of the operad of permuta…
Generation of musical patterns through operads
Samuele Giraudo
We introduce the notion of multi-pattern, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach lies in the fact that this offers a way to compos…
Nonsymmetric operads in combinatorics
Samuele Giraudo
Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form bigger and…
Operads of decorated cliques I: Construction and quotients
Samuele Giraudo
We introduce a functorial construction which takes unitary magmas as input and produces operads. The obtained operads involve configurations of chords la…
The music box operad: Random generation of musical phrases from patterns
Samuele Giraudo
We introduce the notion of multi-patterns, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach in encoding musical phrases lies in the fact tha…