Search Results - "Giraudo, Samuele"

The music box operad: Random generation of musical phrases from patterns by Giraudo, Samuele

“…We introduce the notion of multi-patterns, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach in encoding musical phrases…”
Get full text

Duality of Graded Graphs Through Operads by Giraudo, Samuele

“…Pairs of graded graphs, together with the Fomin property of graded graph duality, are rich combinatorial structures providing among other a framework for…”
Get full text

Cliff operads: a hierarchy of operads on words by Combe, Camille, Giraudo, Samuele

“…A new hierarchy of operads over the linear spans of δ -cliffs, which are some words of integers, is introduced. These operads are intended to be analogues of…”
Get full text

Constructing combinatorial operads from monoids by Giraudo, Samuele

“…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…”
Get full text

Algebraic and combinatorial structures on Baxter permutations by Giraudo, Samuele

“…We give a new construction of a Hopf subalgebra of the Hopf algebra of Free quasi-symmetric functions whose bases are indexed by objects belonging to the…”
Get full text

Algebraic and combinatorial structures on pairs of twin binary trees by Giraudo, Samuele

“…We give a new construction of a Hopf algebra defined first by Reading (2005) [Rea05] whose bases are indexed by objects belonging to the Baxter combinatorial…”
Get full text

Combinatorial operads from monoids by Giraudo, Samuele

“…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…”
Get full text

Operads from posets and Koszul duality by Giraudo, Samuele

“…We introduce a functor As from the category of posets to the category of nonsymmetric binary and quadratic operads, establishing a new connection between these…”
Get full text

Pluriassociative algebras II: The polydendriform operad and related operads by Giraudo, Samuele

“…Dendriform algebras form a category of algebras recently introduced by Loday. A dendriform algebra is a vector space endowed with two nonassociative binary…”
Get full text

Pluriassociative algebras I: The pluriassociative operad by Giraudo, Samuele

“…Diassociative algebras form a category of algebras recently introduced by Loday. A diassociative algebra is a vector space endowed with two associative binary…”
Get full text

Three Fuss-Catalan posets in interaction and their associative algebras by Combe, Camille, Giraudo, Samuele

“…We introduce δ-cliffs, a generalization of permutations and increasing trees depending on a range map δ. We define a first lattice structure on these objects…”
Get full text

Intervals of balanced binary trees in the Tamari lattice by Giraudo, Samuele

“…We show that the set of balanced binary trees is closed by interval in the Tamari lattice. We establish that the intervals [ T , T ′ ] , where T and T ′ are…”
Get full text

Quotients of the Magmatic Operad: Lattice Structures and Convergent Rewrite Systems by Chenavier, Cyrille, Cordero, Christophe, Giraudo, Samuele

“…We study quotients of the magmatic operad that is the free nonsymmetric operad over one binary generator. In the linear setting, we show that the set of these…”
Get full text

Polynomial realizations of Hopf algebras built from nonsymmetric operads by Giraudo, Samuele

“…The natural Hopf algebra $\mathbf{N} \cdot \mathcal{O}$ of an operad $\mathcal{O}$ is a Hopf algebra whose bases are indexed by some words on $\mathcal{O}$. We…”
Get full text

The music box operad: Random generation of musical phrases from patterns by Giraudo, Samuele

“…Journal of Creative Music Systems 8, Issue 1, 2024 We introduce the notion of multi-patterns, a combinatorial abstraction of polyphonic musical phrases. The…”
Get full text

Operads of decorated cliques II: Noncrossing cliques by Giraudo, Samuele

“…S\'eminaire Lotharingien de Combinatoire, B79h, 2023 A complete study of an operad $\mathrm{NC} \mathcal{M}$ of noncrossing configurations of chords introduced…”
Get full text

Polynomial realizations of natural Hopf algebras of nonsymmetric operads by Giraudo, Samuele

“…The natural Hopf algebra $\mathcal{N} \mathcal{O}$ of an operad $\mathcal{O}$ is a Hopf algebra whose bases are indexed by some words on $\mathcal{O}$. We…”
Get full text

Clones of pigmented words and realizations of special classes of monoids by Giraudo, Samuele

“…Clones are generalizations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their…”
Get full text

The combinator ${\bf M}$ and the Mockingbird lattice by Giraudo, Samuele

“…Mathematical Structures in Computer Science, 2022 We study combinatorial and order theoretic structures arising from the fragment of combinatory logic spanned…”
Get full text

Enveloping operads and bicoloured noncrossing configurations by Chapoton, Frédéric, Samuele, Giraudo

“…An operad structure on certain bicoloured noncrossing configurations in regular polygons is studied. Motivated by this study, a general functorial construction…”
Get full text