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Séminaire Algo - Lama Tarsissi
Séminaire Algo - Lama Tarsissi
16-oct.-2018 14:00
Il y a: 33 days

Lama Tarsissi

First Steps in the Algorithmic Reconstruction of Digital Convex Sets

Bâtiment Lavoisier, salle 27? (à confirmer)

A quite remarkable family of discrete sets which has recently attracted the attention of the discrete geometry community is the family of (digitally) convex polyominoes, that are the discrete counterpart of Euclidean convex sets, and combine the natural constraints of convexity and connectedness. A result by Brlek, Lachaud, Provençal and Reutenauer 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 talk is to exploit their reconstruction from orthogonal projections, which has been an open challenge for the last decades. The talk provides some local properties that a boundary word has to fulfill in order to allow a single point modifications that preserves the convexity of the polyomino during the reconstruction process and it provides examples where the addition of one point or two points imposes the inclusion of other points in the neighbor areas, in order to maintain the convexity.

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