59 citations · 217 across the 34 of their papers we have counts for
22 papers · 1 filter
On a Lemma of Schensted
Antoine Abram, Christophe Reutenauer
We give a direct proof of Schensted's lemma asserting that row and column insertion in a tableau commute.
The palindromization map
Dominique Perrin, Christophe Reutenauer
The palindromization map has been defined initially by Aldo de Luca in the context of Sturmian words. It was extended to the free group of rank by Kassel and the second autho W…
The Stylic Monoid
Antoine Abram, Christophe Reutenauer
The free monoid on a finite totally ordered alphabet acts at the left on columns, by Schensted left insertion. This defines a finite monoid, denoted and called…
Primitive Elements of the Hopf Algebras of Tableaux
Claudia Malvenuto, Christophe Reutenauer
The character theory of symmetric groups, and the theory of symmetric functions, both make use of the combinatorics of Young tableaux, such as the Robinson-Schensted algorithm, Sch…
An order on circular permutations
Antoine Abram, Nathan Chapelier-Laget, Christophe Reutenauer
Motivation coming from the study of affine Weyl groups, a structure of ranked poset is defined on the set of circular permutations in (that is, -cycles). It is isomorphic…
Rational series in the free group and the Connes operator
Aaron Lauve, Christophe Reutenauer
We characterize rational series over the free group by using an operator introduced by A. Connes. We prove that rational Malcev--Neumann series posses rational expressions without…
Hall sets, Lazard sets and comma-free codes
Dominique Perrin, Christophe Reutenauer
We investigate the relationship between two constructions of maximal comma-free codes described respectively by Eastman and by Scholtz and the notions of Hall sets and Lazard sets…
Number of right ideals and a -analogue of indecomposable permutations
Roland Bacher, Christophe Reutenauer
We prove that the number of right ideals of codimension in the algebra of noncommutative Laurent polynomials in two variables over the finite field is equal to $…
Bifix codes and interval exchanges
Valérie Berthé, Clelia De Felice, Francesco Dolce +4
We investigate the relation between bifix codes and interval exchange transformations. We prove that the class of natural codings of regular interval echange transformations is clo…
Return words of linear involutions and fundamental groups
Valérie Berthé, Vincent Delecroix, Francesco Dolce +3
We investigate the natural codings of linear involutions. We deduce from the geometric representation of linear involutions as Poincaré maps of measured foliations a suitable defin…
Notes on sets of first return
Valérie Berthé, Clelia De Felice, Francesco Dolce +3
We prove in this note that, for an alphabet with three letters, the set of first return to a given word in a set satisfying the tree condition is a basis of the free group.
Maximal bifix decoding
Valérie Berthé, Clelia De Felice, Francesco Dolce +4
We introduce a class of sets of words which is a natural common generalization of Sturmian sets and of interval exchange sets. This class of sets consists of the uniformly recurren…
Acyclic, connected and tree sets
Valerie Berthé, Clelia De Felice, Francesco Dolce +4
Given a set of words, one associates to each word in an undirected graph, called its extension graph, and which describes the possible extensions of on the left and…
Algebraicity of the zeta function associated to a matrix over a free group algebra
Christian Kassel, Christophe Reutenauer
Following and generalizing a construction by Kontsevich, we associate a zeta function to any matrix with entries in a ring of noncommutative Laurent polynomials with integer coeffi…
The Reciprocal of for non-commuting and , Catalan numbers and non-commutative quadratic equations
Arkady Berenstein, Vladimir Retakh, Christophe Reutenauer +1
The aim of this paper is to describe the inversion of the sum where and are non-commuting variables as a formal series in and . We show that t…
Bifix codes and Sturmian words
Jean Berstel, Clelia De Felice, Dominique Perrin +2
We prove new results concerning the relation between bifix codes, episturmian words and subgroups offree groups. We study bifix codes in factorial sets of words. We generalize most…
On the superimposition of Christoffel words
Geneviève Paquin, Christophe Reutenauer
Initially stated in terms of Beatty sequences, the Fraenkel conjecture can be reformulated as follows: for a -letter alphabet A, with a fixed , there exists a unique b…
-Tiling of the Plane
Francois Bergeron, Christophe Reutenauer
We study properties of (bi-infinite) arrays having all adjacent adjacent minors equal to one. If we further add the condition that all adjacent mino…
Generalized descent patterns in permutations and associated Hopf algebras
J. -C. Novelli, C. Reutenauer, J. -Y. Thibon
Descents in permutations or words are defined from the relative position of two consecutive letters. We investigate a statistic involving patterns of k consecutive letters, and sho…
A palindromization map for the free group
Christian Kassel, Christophe Reutenauer
We define a self-map Pal: F_2 --> F_2 of the free group on two generators a, b, using automorphisms of F_2 that form a group isomorphic to the braid group B_3. The map Pal restrict…
P-partitions and a multi-parameter Klyachko idempotent
Peter McNamara, Christophe Reutenauer
Because they play a role in our understanding of the symmetric group algebra, Lie idempotents have received considerable attention. The Klyachko idempotent has attracted interest f…
Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables
Nantel Bergeron, Christophe Reutenauer, Mercedes Rosas +1
We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions which was recently studied as a vector space by Rosas and Sagan. The bases for this…