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

Breen, Marilyn. "Sets Expressible as Unions of Staircase $n$-Convex Polygons." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 50.1 (2011): 23-28. <http://eudml.org/doc/197243>.

@article{Breen2011,
abstract = {Let $k$ and $n$ be fixed, $k\ge 1$, $n \ge 1$, 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 $P_i$, $1 \le i \le k$.},
author = {Breen, Marilyn},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {orthogonal polygons; staircase $n$-convex polygons; orthogonal polygons; staircase -convex polygons},
language = {eng},
number = {1},
pages = {23-28},
publisher = {Palacký University Olomouc},
title = {Sets Expressible as Unions of Staircase $n$-Convex Polygons},
url = {http://eudml.org/doc/197243},
volume = {50},
year = {2011},
}

TY - JOUR
AU - Breen, Marilyn
TI - Sets Expressible as Unions of Staircase $n$-Convex Polygons
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2011
PB - Palacký University Olomouc
VL - 50
IS - 1
SP - 23
EP - 28
AB - Let $k$ and $n$ be fixed, $k\ge 1$, $n \ge 1$, 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 $P_i$, $1 \le i \le k$.
LA - eng
KW - orthogonal polygons; staircase $n$-convex polygons; orthogonal polygons; staircase -convex polygons
UR - http://eudml.org/doc/197243
ER -