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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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: How should one select an $ l$-element subset of a rectangular array of lattice points (points with integral coordinates) in $ n$-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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DOI: https://doi.org/10.1090/S0002-9939-1971-0270923-7
Keywords: Lattice points, maximal number of edges, generalized Macaulay theorem, $ n$-dimensional Euclidean space
Article copyright: © Copyright 1971 American Mathematical Society