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Packing tripods : narrowing the density gap
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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 ISSN 0012-365X.
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Official URL: http://dx.doi.org/10.1016/j.disc.2004.12.028
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 | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||||
Journal or Publication Title: | Discrete Mathematics | ||||||||
Publisher: | Elsevier BV | ||||||||
ISSN: | 0012-365X | ||||||||
Official Date: | 28 July 2007 | ||||||||
Dates: |
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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 | ||||||||
Date of first compliant deposit: | 15 December 2015 | ||||||||
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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