English

Digital Convexity and Combinatorics on Words

Combinatorics 2025-03-12 v2 Discrete Mathematics Formal Languages and Automata Theory

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.

Keywords

Cite

@article{arxiv.2502.19926,
  title  = {Digital Convexity and Combinatorics on Words},
  author = {Alessandro De Luca and Gabriele Fici and Andrea Frosini},
  journal= {arXiv preprint arXiv:2502.19926},
  year   = {2025}
}

Comments

Extended version of a manuscript submitted to WORDS 2025. arXiv admin note: text overlap with arXiv:2211.09417

R2 v1 2026-06-28T21:59:53.630Z