We give a new characterization of maximal repetitions (or runs) in strings based on Lyndon
words. The characterization leads to a proof of what was known as the “runs” conjecture RM …

In 1875, Elwin Bruno Christoffel introduced a special class of words on a binary alphabet
linked to continued fractions which would go onto be known as Christoffel words. Some …

We give a new characterization of maximal repetitions (or runs) in strings, using a tree
defined on recursive standard factorizations of Lyndon words, called the Lyndon tree. The …

A generalized lexicographical order on infinite words is defined by choosing for each
position a total order on the alphabet. This allows to define generalized Lyndon words …

Continued fractions with 𝑆𝐿(2,𝑍)-branches: combinatorics and entropy Page 1
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 370, Number 7 …

Lyndon factorization and Lempel-Ziv (LZ) factorization are both important tools for analysing
the structure and complexity of strings, but their combinatorial structure is very different. In …

This paper proposes full convexity as an alternative definition of digital convexity, which is
valid in arbitrary dimension. It solves many problems related to its usual definitions, like …

Rigid motions (ie transformations based on translations and rotations) are simple, yet
important, transformations in image processing. In R^ n R n, they are both topology and …

Abstract The Minimum Length Polygon (MLP) is an interesting first order approximation of a
digital contour. For instance, the convexity of the MLP is characteristic of the digital convexity …

We present two efficient algorithms which, given a compressed representation of a string w
of length N, compute the Lyndon factorization of w. Given a straight line program (SLP) S of …