Two- and three-dimensional rectangular dissections are considered as sets of intersecting line and plane segments. The different types of intersections, or joints, are enumerated and various properties considered.
Get full access to this article
View all access options for this article.
References
1.
BanhamR, 1960Theory and Design in the First Machine Age (Architectural Press, London)
2.
BiggsN, 1969“Rectangulations”Proceedings of the Cambridge Philosophical Society65399–408
3.
BlochC J, 1976“On the set and number of minimal gratings for rectangular dissections”Environment and Planning B371–74
4.
BlochC JKrishnamurtiR, 1978“The counting of rectangular dissections”Environment and Planning B5207–214
5.
de BruijnN G, 1969“Filling boxes with bricks”American Mathematical Monthly7637–40
6.
EarlC F, 1977“A note on the generation of rectangular dissections”Environment and Planning B4241–246
7.
FlemmingU, 1978“Wall representations of rectangular dissections and their use in automated space allocation”Environment and Planning B5215–232
8.
KatonaGSzaszD, 1971“Matching problems”Journal of Combinatorial Theory, Series B1060–92
9.
KlarnerD, 1967“Cell growth problems”Canadian Journal of Mathematics19851–863
10.
KlarnerDGöbelF, 1969“Packing boxes with congruent figures”Indagationes Mathematicae31465–472
11.
KrishnamurtiRRoeP H O'N, 1978“Algorithmic aspects of plan generation and enumeration”Environment and Planning B5157–177
