Abstract
Digital convex (DC) sets plays a prominent role in the framework of digital geometry providing a natural generalization to the concept of Euclidean convexity when we are dealing with polyominoes, i.e., finite and connected sets of points. A result by Brlek, Lachaud, Provençal and Reutenauer (see [4]) on this topic sets a bridge between digital convexity and combinatorics on words: the boundary word of a DC polyomino can be divided in four monotone paths, each of them having a Lyndon factorization that contains only Christoffel words.
The intent of this paper is to provide some local properties that a boundary words has to fulfill in order to allow a single point modifications that preserves the convexity of the polyomino.
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Acknowledgment
This study has been partially supported by INDAM - GNCS Project 2017.
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Dulio, P., Frosini, A., Rinaldi, S., Tarsissi, L., Vuillon, L. (2017). First Steps in the Algorithmic Reconstruction of Digital Convex Sets. In: Brlek, S., Dolce, F., Reutenauer, C., Vandomme, É. (eds) Combinatorics on Words. WORDS 2017. Lecture Notes in Computer Science(), vol 10432. Springer, Cham. https://doi.org/10.1007/978-3-319-66396-8_16
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DOI: https://doi.org/10.1007/978-3-319-66396-8_16
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