An upward (resp. downward) digitally convex word is a binary word that best approximates from below (resp. from above) an upward (resp. downward) convex curve in the plane. We study these words from the combinatorial point of view, formalizing their geometric properties and highlighting connections with Christoffel words and finite Sturmian words. In particular, we study from the combinatorial perspective the operations of inflation and deflation on digitally convex words.
De Luca, A., Fici, G., Frosini, A. (2025). Digital Convexity and Combinatorics on Words. In G. Gamard, J. Leroy (a cura di), Combinatorics on Words 15th International Conference, WORDS 2025, Nancy, France, June 30 – July 4, 2025, Proceedings (pp. 91-103). Springer [10.1007/978-3-031-97548-6_9].
Digital Convexity and Combinatorics on Words
Fici G.;
2025-01-01
Abstract
An upward (resp. downward) digitally convex word is a binary word that best approximates from below (resp. from above) an upward (resp. downward) convex curve in the plane. We study these words from the combinatorial point of view, formalizing their geometric properties and highlighting connections with Christoffel words and finite Sturmian words. In particular, we study from the combinatorial perspective the operations of inflation and deflation on digitally convex words.
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