Combinatorial Variations on Cantor's Diagonal

We discuss counting problems linked to finite versions of Cantor's diagonal of infinite tableaux. We extend previous results of [2] by refining an equivalence relation that reduces significantly the exhaustive generation. New enumerative results follow and allow to look at the sub-class of the so- called bi-Cantorian tableaux. We conclude with a correspondence between Cantorian-type tableaux and coloring of hypergraphs having a square number of vertices

Palindromic complexity of codings of rotations

International audienceWe study the palindromic complexity of infinite words obtained by coding rotations on partitions of the unit circle by inspecting the return words. The main result is that every coding of rotations on two intervals is full, that is, it realizes the maximal palindromic complexity. As a byproduct, a slight improvement about return words in codings of rotations is obtained: every factor of a coding of rotations on two intervals has at most 4 complete return words, where the bound is realized only for a finite number of factors. We also provide a combinatorial proof for the special case of complementary-symmetric Rote sequences by considering both palindromes and antipalindromes occurring in it

Properties of the extremal infinite smooth words

Smooth words are connected to the Kolakoski sequence. We construct the maximal and the minimal in nite smooth words, with respect to the lexicographical order. The naive algorithm generating them is improved by using a reduction of the De Bruijn graph of their factors. We also study their Lyndon factorizations. Finally, we show that the minimal smooth word over the alphabet f1; 3g belongs to the orbit of the Fibonacci word

On the critical exponent of generalized Thue-Morse words

Automata, Logic and Semantic

Exhaustive generation of atomic combinatorial differential operators

Labelle and Lamathe introduced in 2009 a generalization of the standard combinatorial differential species operator D, by giving a combinatorial interpretation to Ω(X, D)F(X), where Ω(X, T) and F(X) are two-sort and one-sort species respectively. One can show that such operators can be decomposed as sums of products of simpler operators called atomic combinatorial differential operators. In their paper, Labelle and Lamathe presented a list of the first atomic differential operators. In this paper, we describe an algorithm that allows to generate (and enumerate) all of them, subject to available computer resources. We also give a detailed analysis of how to compute the molecular components of Ω(X, D)F(X)

A new vincular pattern based Mahonian statistic on words

International audienc