Related papers: Philippe Flajolet's early work in combinatorics
This thesis comes within the scope of algebraic combinatorics and studies problems related to three orders on permutations: the two said weak orders (right and left) and the strong order or Bruhat order. The first part deals with bases of…
This article presents the \emph{Serial and Unserial Methods} (SUM). The algorithms are strongly related to the first part of a classical reference in combinatorics, the \emph{Combinatorial algorithms for computers and calculators}, from…
We discuss the role of combinators in the development of the modern conception of computation over the course of the past century. We describe how ideas about formalism and mathematical logic led to the introduction of combinators in 1920…
Combinatorial interpretation of the fibonomial coefficients recently proposed by the present author results here in combinatorial interpretation of the recurrence relation for fibonomial coefficients . The presentation is provided with…
This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…
This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…
In light of the grammar given by Ji for the $(\alpha,\beta)$-Eulerian polynomials introduced by Carlitz and Scoville, we provide a labeling scheme for increasing binary trees. In this setting, we obtain a combinatorial interpretation of the…
The purpose of the present work is to provide short and supple teaching notes for a $30$ hours introductory course on elementary \textit{Enumerative Algebraic Combinatorics}. We fully adopt the \textit{Rota way}. The themes are organized…
This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is…
Time series segmentation is one of the many data mining tools. This paper, in French, takes local extrema as perceptually interesting points (PIPs). The blurring of those PIPs by the quick fluctuations around any time series is treated via…
This paper intends to survey the vast literature devoted to a problem posed by Wilf in 1978 which, despite the attention it attracted, remains unsolved. As it frequently happens with combinatorial problems, many researchers who got involved…
About twenty years ago, Green wrote a survey article on the utility of looking at toy versions over finite fields of problems in additive combinatorics. This article was extremely influential, and the rapid development of additive…
Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus…
Generating series are crucial in enumerative combinatorics, analytic combinatorics, and combinatorics on words. Though it might seem at first view that generating Dirichlet series are less used in these fields than ordinary and exponential…
A powerful statistical interpolating concept, which we call \emph{fully lifted} (fl), is introduced and presented while establishing a connection between bilinearly indexed random processes and their corresponding fully decoupled (linearly…
We present new, exceptionally efficient proofs of Poisson--Dirichlet limit theorems for the scaled sizes of irreducible components of random elements in the classic combinatorial contexts of arbitrary assemblies, multisets, and selections,…
Let $\Phi$ be a root system. Postnikov introduced and studied the mixed $\Phi$-Eulerian numbers. These numbers indicate the mixed volumes of $\Phi$-hypersimplices. As specializations of these numbers, one can obtain the usual Eulerian…
In this talk, we are concerned with the formulation and understanding of the combinatorics of time-ordered n-point functions in terms of the Hopf algebra of field operators. Mathematically, this problem can be formulated as one in…
Integer compositions with certain colored parts were introduced by Andrews in 2007 to address a number-theoretic problem. Integer compositions allowing zero as some parts were introduced by Ouvry and Polychronakos in 2019. We give a…
This paper synergizes the roles of adjoint in various disciplines of mathematics, sciences, and engineering. Though the materials developed and presented are not new -- as each or some could be found in (or inferred from) publications in…