Related papers: Colored operads, series on colored operads, and co…
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 that it becomes possible to compose multi-patterns in order to…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
The main ideas developed in this habilitation thesis consist in endowing combinatorial objects (words, permutations, trees, Young tableaux, etc.) with operations in order to construct algebraic structures. This process allows, by studying…
We give an explicit construction of the generating set of a colored operad that implements theta theory in the mathematical model of Minimalism in generative linguistics, in the form of a coloring algorithm for syntactic objects. We show…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…
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…
In this paper, we give a general framework for the Boltzmann generation of colored objects belonging to combinatorial constructible classes. We propose an intuitive notion called profiled objects which allows the sampling of size-colored…
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 compose two multi-patterns in order to produce a longer one. This…
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…
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 more complex ones. Coming historically from algebraic…
Let A be a class of objects, equipped with an integer size such that for all n the number a(n) of objects of size n is finite. We are interested in the case where the generating fucntion sum_n a(n) t^n is rational, or more generally…
Asymptotic expansions of Gaussian integrals may often be interpreted as generating functions for certain combinatorial objects (graphs with additional data). In this article we discuss a general approach to all such cases using colored…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
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 prototypical example is the one of the Young graded graph of integer…
We generalize the construction of multitildes in the aim to provide multitilde operators for regular languages. We show that the underliying algebraic structure involves the action of some operads. An operad is an algebraic structure that…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
We continue to consider the ordered lexicographic sequence, which is constructed according to the formal characteristics of a series of natural numbers. For analysis, we selected balanced parentheses with zeros, Motzkin words. As you know,…
We begin a systematic study of the enumerative combinatorics of mixed succession rules, which are succession rules such that, in the associated generating tree, the nodes are allowed to produce their sons at several different levels…