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On the number of regular configurations

✍ Scribed by Yunshyong Chow

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
426 KB
Volume
66
Category
Article
ISSN
0012-365X

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✦ Synopsis

A necessary and sufficient graph-theoretic condition is given for the number of different colorings, or regular configurations, on lattice points 1, 2,..., n in R to grow exponentially in n. This condition also characterizes when the largest eigenvalue of a zero-one matrix is greater than one. A similar but different condition is obtained for the coloring problem on the lattice points in R d, d >I 2, with the hypercubic lattice structure.

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