Guarding polyominoes, polycubes and polyhypercubes
Resource type
Author/contributor
- Pinciu, Val (Author)
Title
Guarding polyominoes, polycubes and polyhypercubes
Abstract
We consider variations of the original art gallery problem where the domain is a polyomino, a polycube, or a polyhypercube. An m-polyomino is the connected union of m unit squares called pixels, an m-polycube is the connected union of m unit cubes called voxels, and an m-polyhypercube is the connected union of m unit hypercubes in a d dimensional Euclidean space. In this paper we generalize and unify the known results about guarding polyominoes and polycubes and obtain simpler proofs. We also obtain new art gallery theorems for guarding polyhypercubes. © 2015 Elsevier B.V.
Publication
Electronic Notes in Discrete Mathematics
Date
2015
Volume
49
Pages
159-166
Journal Abbr
Electron. Notes Discrete Math.
Citation Key
pop00392
ISSN
15710653 (ISSN)
Language
English
Extra
2 citations (Crossref) [2023-10-31]
Citation Key Alias: lens.org/069-553-586-251-759
tex.type: [object Object]
Citation
Pinciu, V. (2015). Guarding polyominoes, polycubes and polyhypercubes. Electronic Notes in Discrete Mathematics, 49, 159–166. https://doi.org/10.1016/j.endm.2015.06.024
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