Sets of lattice points which contain a maximal number of edges

Author:
G. F. Clements

Journal:
Proc. Amer. Math. Soc. **27** (1971), 13-15

MSC:
Primary 05.04

DOI:
https://doi.org/10.1090/S0002-9939-1971-0270923-7

MathSciNet review:
0270923

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Abstract | References | Similar Articles | Additional Information

Abstract: How should one select an -element subset of a rectangular array of lattice points (points with integral coordinates) in -dimensional Euclidean space so as to include the largest possible number of edges (pairs of points differing in exactly one coordinate)? It is shown that the generalized Macaulay theorem due to the author and B. Lindström contains the (known) solution.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1971-0270923-7

Keywords:
Lattice points,
maximal number of edges,
generalized Macaulay theorem,
-dimensional Euclidean space

Article copyright:
© Copyright 1971
American Mathematical Society