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.
Digital Convexity and Combinatorics on Words / De Luca, Alessandro; Fici, Gabriele; Frosini, Andrea. - 15729 LNCS:(2025), pp. 91-103. ( 15th International Conference on Combinatorics on Words, WORDS 2025 Nancy, France 2025) [10.1007/978-3-031-97548-6_9].
Digital Convexity and Combinatorics on Words
De Luca, Alessandro
;
2025
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.| File | Dimensione | Formato | |
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