Tiskin, Alexander (2007) Packing tripods : narrowing the density gap. Discrete Mathematics, Volume 307 (Number 16). pp. 1973-1981. doi:10.1016/j.disc.2004.12.028

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Abstract

In 1984, Stein and his co-authors posed a problem concerning simple three-dimensional shapes, known as semicrosses, or tripods. By definition, a tripod of order n is formed by a corner and the three adjacent edges of an integer n x n x n cube. How densely can one fill the space with non-overlapping tripods of a given order? In particular, is it possible to fill a constant fraction of the space as tripod order tends to infinity? In this paper, we settle the second question in the negative: the fraction of the space that can be filled with tripods must be infinitely small as the order grows. We also make a step towards the solution of the first question, by improving the currently known asymptotic lower bound on tripod packing density, and by presenting some computational results on low-order packings.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Computer Science
Journal or Publication Title:	Discrete Mathematics
Publisher:	Elsevier BV
ISSN:	0012-365X
Official Date:	28 July 2007
Dates:	Date Event 28 July 2007 Published 12 December 2004 Accepted 8 September 2003 Submitted
Volume:	Volume 307
Number:	Number 16
Number of Pages:	9
Page Range:	pp. 1973-1981
DOI:	10.1016/j.disc.2004.12.028
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Title of Event:	European Conference on Combinatorics, Graph Theory and Applications
Location of Event:	Prague, Czech Republic
Date(s) of Event:	September 08-12, 2003

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