Digital Convexity and Combinatorics on Words
arXiv:2502.19926
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.
Extended version of a manuscript submitted to WORDS 2025. arXiv admin note: text overlap with arXiv:2211.09417