Name
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 nxnxn 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. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.disc.2004.12.028 | Discrete Mathematics |
Keywords | Field | DocType |
semicross packing,regularity lemma,tripod packing,lower bound,three dimensional | Integer,Discrete mathematics,Combinatorics,Sphere packing,Upper and lower bounds,Infinity,Tripod (photography),Mathematics,Cube | Journal |
Volume | Issue | ISSN |
307 | 16 | Discrete Mathematics |
Citations | PageRank | References |
1 | 0.63 | 6 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexander Tiskin | 1 | 220 | 15.50 |