On the factors of the Sturmian sequences
Theoretical Computer Science
On the number of factors of Sturmian words
Theoretical Computer Science
Combinatorics of patterns of a bidimensional Sturmian sequence.
Theoretical Computer Science
Theoretical Computer Science
Balanced sequences and optimal routing
Journal of the ACM (JACM)
Fraenkel's conjecture for six sequences
Discrete Mathematics
Episturmian words and some constructions of de Luca and Rauzy
Theoretical Computer Science
Generalized balances in Sturmian words
Discrete Applied Mathematics
Balances for fixed points of primitive substitutions
Theoretical Computer Science - WORDS
Lattices and multi-dimensional words
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Plane digitization and related combinatorial problems
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Maximal pattern complexity of two-dimensional words
Theoretical Computer Science
Discrete Applied Mathematics
Plane digitization and related combinatorial problems
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
| Hi-index | 5.23 |
A word u is called 1-balanced if for any two factors v and w of u of equal length, we have 1|v|i|w|i1 for each letter i, where |v|i denotes the number of occurrences of i in the factor v. The aim of this paper is to extend the notion of balance to multi-dimensional words. We first characterize all 1-balanced words on &Zn. In particular, we prove they are fully periodic for n1. We then give a quantitative measure of non-balancedness for some words on &Z2 with irrational density, including two-dimensional Sturmian words.