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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;
refs;
listen;
history;
text;
internal format)
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OFFSET
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3,1
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COMMENTS
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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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Table of n, a(n) for n=3..32.
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: A187824 A177028 A162552 * A217031 A104136 A198466
Adjacent sequences: A133572 A133573 A133574 * 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, Sep 17 2007
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STATUS
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approved
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