

A133575


Table, read by rows, giving the number of vertices possible in 2 X n nondegenerate classical transportation polytopes.


1



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
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OFFSET

3,1


COMMENTS

This paper discusses properties of the graphs of 2way and 3way transportation polytopes, in particular, their possible numbers of vertices and their diameters. Our main results include a quadratic bound on the diameter of axial 3way transportation polytopes and a catalog of nondegenerate transportation polytopes of small sizes. The catalog disproves five conjectures about these polyhedra stated in the monograph by Yemelichev et al. (1984). It also allowed us 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.


LINKS

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, arXiv:0709.2189 [math.CO], 20072009, tables p. 4.


EXAMPLE

Table 1 of De Loera et al.
size dimensionPossible numbers of vertices
2.X.3....2....3.4..5..6
2.X.4....3....4.6..8.10.12
2.X.5....4....5.8.11.12.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30


CROSSREFS

Cf. A133575, A133576, A133577.
Sequence in context: A187824 A177028 A162552 * A230113 A217031 A104136
Adjacent sequences: A133572 A133573 A133574 * A133576 A133577 A133578


KEYWORD

nonn,tabf,more


AUTHOR

Jonathan Vos Post, Sep 17 2007


STATUS

approved



