An introduction to balanced sequential arrays on the square grid

Street, Anne Penfold and Nester, Marks R. (2009) An introduction to balanced sequential arrays on the square grid. Mathematica Slovaca, 59 2: 177-192. doi:10.2478/s12175-009-0116-5

Author Street, Anne Penfold
Nester, Marks R.
Title An introduction to balanced sequential arrays on the square grid
Journal name Mathematica Slovaca   Check publisher's open access policy
ISSN 0139-9918
Publication date 2009-03-13
Sub-type Article (original research)
DOI 10.2478/s12175-009-0116-5
Volume 59
Issue 2
Start page 177
End page 192
Total pages 16
Editor Sylvia Pulmannova
Place of publication Poland
Publisher Versita
Collection year 2010
Language eng
Subject C1
970101 Expanding Knowledge in the Mathematical Sciences
010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)
Formatted abstract
Plants grown in large numbers for commercial purposes are usually set out on a regular grid, triangular, square or hexagonal, or possibly a rectangular grid. We need to understand their behaviour when they compete with each other for light, water and nutrients. In a greenhouse, there may be a lamp over each plant, half the plants having their lamps on and half off. The intensity of light falling on any particular plant is determined mainly by whether its own lamp is on, next by the number of its nearest neighbours whose lamps are on, and perhaps also by the number of its second-nearest neighbours whose lamps are on.
Such arrays are also used to study competition among different types of plants and, with some extra restrictions, to design field layouts as well. The problem of constructing suitable arrays was introduced in [CORMACK, R. M.: Spatial aspects of competition beween individuals. In: Spatial and Temporal Analysis in Ecology (R. M. Cormack and J. K. Ord, eds.), International Co-operative Publishing House, Fairland, Maryland, USA, 1979] and discussed in [GATES, D. J.: Competition between two types of plants with specified neighbour configurations, Math. Biosci. 48 (1980), 195–209]. Here we consider only the square grid.
Keyword balanced arrays
sequential arrays
binary arrays
regular grids
square grids
Q-Index Code C1
Q-Index Status Confirmed Code

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2010 Higher Education Research Data Collection
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Created: Thu, 01 Apr 2010, 12:34:29 EST by Kay Mackie on behalf of School of Mathematics & Physics