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Semi-monotone sets

Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov (2013)

Journal of the European Mathematical Society

A coordinate cone in $ℝ^{n}$ is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of $ℝ^{n}$ , definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone...

Séparation forte $k$ -branlante de deux convexes

Jacques Bair (1977)

Commentationes Mathematicae Universitatis Carolinae

Sets Expressible as Unions of Staircase $n$ -Convex Polygons

Marilyn Breen (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Let $k$ and $n$ be fixed, $k \geq 1$ , $n \geq 1$ , and let $S$ be a simply connected orthogonal polygon in the plane. For $T \subseteq S, T$ lies in a staircase $n$ -convex orthogonal polygon $P$ in $S$ if and only if every two points of $T$ see each other via staircase $n$ -paths in $S$ . This leads to a characterization for those sets $S$ expressible as a union of $k$ staircase $n$ -convex polygons $P_{i}$ , $1 \leq i \leq k$ .

Displaying 1 – 9 of 9

Semi-monotone sets

Séparation forte $k$ -branlante de deux convexes

Sets Expressible as Unions of Staircase $n$ -Convex Polygons

Shaking compact sets.

Shortest Watchman Routes in Simple Polygons.

Stabilité isopérimétrique

Staircase Kernels for Orthogonal d-Polytopes.

Starshapedness in convexity spaces

Streckenförmigkeit - eine weitere Verallgemeinerung der Sternförmigkeit

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