Some combinatorial properties of Sturmian words
Theoretical Computer Science
Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
Sturmian words, Lyndon words and trees
Theoretical Computer Science
Digital lines and digital convexity
Digital and image geometry
Lyndon + Christoffel = digitally convex
Pattern Recognition
| Hi-index | 5.23 |
Using a combinatorial characterization of digital convexity based on words, one defines the language of convex words. The complement of this language forms an ideal whose minimal elements, with respect to the factorial ordering, appear to have a particular combinatorial structure very close to the Christoffel words. In this paper, those words are completely characterized as those of the form uw^kv where k=1, w=u@?v and u,v,w are Christoffel words. Also, by considering the most balanced among the unbalanced words, we obtain a second characterization for a special class of minimal non-convex words that are of the form u^2v^2 corresponding to the case k=1 in the previous form.