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The number of configurations of molecules on a lattice

โœ Scribed by Miller, A. R.


Book ID
118050914
Publisher
Cambridge University Press
Year
1946
Tongue
English
Weight
813 KB
Volume
42
Category
Article
ISSN
0305-0041

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When a strictly convex plane set S moves by translation, the set J of points of the integer lattice that lie in S changes. The number K of equivalence classes of sets J under lattice translations (configurations) is bounded in terms of the area of the Brunn-Minkowski difference set of S. If S satisf

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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 sim