60 citations · 179 across the 42 of their papers we have counts for
42 papers
Generating naturally labeled posets through matrix extensions, order ideals and automorphism groups
Gi-Sang Cheon, Samuele Giraudo, Gukwon Kwon +1
We propose a matrix approach for generating naturally labeled posets by representing each poset on the set as a Boolean poset matrix . This algebraic representation en…
Fundamental and homogeneous bases of Hopf algebras built from nonsymmetric operads
Samuele Giraudo
We introduce new partial order structures on the underlying sets of free nonsymmetric operads. These posets involve decorated ordered rooted trees, and their terminal intervals are…
Polynomial realizations of Hopf algebras built from nonsymmetric operads
Samuele Giraudo
The natural Hopf algebra of an operad is a Hopf algebra whose bases are indexed by some words on . We construct polynomial…
Operads of decorated cliques II: Noncrossing cliques
Samuele Giraudo
A complete study of an operad of noncrossing configurations of chords introduced in previous work of the author is performed. This operad is defined on th…
Operad Structure of Poset Matrices
Arnauld Mesinga Mwafise, Gi-Sang Cheon, Hong Joon Choi +1
This paper examines operad structures derived from poset matrices by formulating a set of new construction rules for poset matrices. In this direction, eleven different partial com…
Polynomial realizations of natural Hopf algebras of nonsymmetric operads
Samuele Giraudo
The natural Hopf algebra of an operad is a Hopf algebra whose bases are indexed by some words on . We introduce new bases of th…
Two associative operads of packed words
Samuele Giraudo, Yannic Vargas
The associative operad is a central structure in operad theory, defined on the linear span of the set of permutations. We build two analogs of the associative operad on the linear…
Clones of pigmented words and realizations of special classes of monoids
Samuele Giraudo
Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in th…
The combinator and the Mockingbird lattice
Samuele Giraudo
We study combinatorial and order theoretic structures arising from the fragment of combinatory logic spanned by the basic combinator . This basic combinator, named as the…
Mockingbird lattices
Samuele Giraudo
We study combinatorial and order theoretic structures arising from the fragment of combinatory logic spanned by the basic combinator . This basic combinator, named as the…
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…
Three Fuss-Catalan posets in interaction and their associative algebras
Camille Combe, Samuele Giraudo
We introduce -cliffs, a generalization of permutations and increasing trees depending on a range map . We define a first lattice structure on these objects and we establish g…
Duality of graded graphs through operads
Samuele Giraudo
Pairs of graded graphs, together with the Fomin property of graded graph duality, are rich combinatorial structures providing among other a framework for enumeration. The prototypi…
Graph insertion operads
Jean-Christophe Aval, Samuele Giraudo, Théo Karaboghossian +1
Using the combinatorial species setting, we propose two new operad structures on multigraphs and on pointed oriented multigraphs. The former can be considered as a canonical operad…
Three interacting families of Fuss-Catalan posets
Camille Combe, Samuele Giraudo
Three families of posets depending on a nonnegative integer parameter are introduced. The underlying sets of these posets are enumerated by the -Fuss Catalan numbers. Among…
Operads on graphs: extending the pre-Lie operad and general construction
Jean-Christophe Aval, Samuele Giraudo, Théo Karaboghossian +1
The overall aim of this paper is to define a structure of graph operads, thus generalizing the celebrated pre-Lie operad on rooted trees. More precisely, we define two operads on m…
Tree series and pattern avoidance in syntax trees
Samuele Giraudo
A syntax tree is a planar rooted tree where internal nodes are labeled on a graded set of generators. There is a natural notion of occurrence of contiguous pattern in such trees. W…
Quotients of the magmatic operad: lattice structures and convergent rewrite systems
Cyrille Chenavier, Christophe Cordero, Samuele Giraudo
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 quotients admits a l…
Generalizations of the associative operad and convergent rewrite systems
Cyrille Chenavier, Christophe Cordero, Samuele Giraudo
The associative operad is the quotient of the magmatic operad by the operad congruence identifying the two binary trees of degree . We introduce here a generalization of the ass…
Algorithmic and algebraic aspects of unshuffling permutations
Samuele Giraudo, Stéphane Vialette
A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuf…