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Search: id:A133575
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| A133575 |
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Table, read by rows, of the number of vertices possible in 2 X n nondegenerate classical transportation polytopes. |
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1
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| 3, 4, 5, 6, 4, 6, 8, 10, 12, 5, 8, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30
(list; table; graph; listen)
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OFFSET
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3,1
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COMMENT
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This paper discusses properties of the graphs of 2-way and 3-way transportation polytopes, in particular, their possible numbers of vertices and their diameters. Our main results include a quadratic bound on the diameter of axial 3-way transportation polytopes and a catalogue of non-degenerate transportation polytopes of small sizes. The catalogue disproves five conjectures about these polyhedra stated in the monograph by Yemelichev et al. (1984). It also allowed to discover some new results. For example, we prove that the number of vertices of an m x n transportation polytope is a multiple of the greatest common divisor of m and n.
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LINKS
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J. A. De Loera, Edward D. Kim, Shmuel Onn and Francisco Santos, Graphs of Transportation Polytopes, tables p. 4.
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EXAMPLE
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Table 1 of De Loera et al.
size|dimension|Possible numbers of vertices
2X3..|...2....|3.4..5..6
2X4..|...3....|4.6..8.10.12
2X5..|...4....|5.8.11.12.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30
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CROSSREFS
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Cf. A133575, A133576, A133577.
Sequence in context: A103606 A139794 A004484 this_sequence A104136 A036288 A049267
Adjacent sequences: A133572 A133573 A133574 this_sequence A133576 A133577 A133578
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KEYWORD
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nonn,tabl
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 17 2007
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