LP-orientations of cubes and crosspolytopes
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| 024 | 7 | 0 | |a 10.1515/advg.2004.4.4.459 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.1515/advg.2004.4.4.459 | ||
| 100 | 1 | |a Develin |D Mike | |
| 245 | 1 | 0 | |a LP-orientations of cubes and crosspolytopes |h [Elektronische Daten] |c [Mike Develin] |
| 520 | 3 | |a In a paper presented at a 1996 conference, Holt and Klee introduced a set of necessary conditions for an orientation of the graph of a d-polytope to be induced by a realization into ℝ n and a linear function on that space. In general, it is an open question to decide whether for a polytope P every orientation of its graph satisfying these conditions can in fact be realized in this fashion; two natural families of polytopes to consider are cubes and crosspolytopes. For cubes, we show that, as n grows, the percentage of n-cube Holt-Klee orientations which can be realized goes asymptotically to 0. For crosspolytopes, we give a stronger set of conditions which are both necessary and sufficient for an orientation to be in this class; as a corollary, we prove that all shellings of cubes are line shellings. | |
| 540 | |a © de Gruyter | ||
| 690 | 7 | |a Geometry |2 nationallicence | |
| 773 | 0 | |t Advances in Geometry |d Walter de Gruyter |g 4/4(2004-11-03), 459-468 |x 1615-715X |q 4:4<459 |1 2004 |2 4 |o advg | |
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| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/advg.2004.4.4.459 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Develin |D Mike | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Advances in Geometry |d Walter de Gruyter |g 4/4(2004-11-03), 459-468 |x 1615-715X |q 4:4<459 |1 2004 |2 4 |o advg | ||
| 900 | 7 | |b CC0 |u http://creativecommons.org/publicdomain/zero/1.0 |2 nationallicence | |
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| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||