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Proceedings of the American Mathematical Society

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



Dual necklaces of $ n$-dimensional cubes

Author: Kenneth Kalmanson
Journal: Proc. Amer. Math. Soc. 31 (1972), 511-516
MathSciNet review: 0285993
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Abstract | References | Additional Information

Abstract: It has been shown that certain finite configurations, called dual necklaces, of euclidean spheres yield information on longest rectilinear circuits on the sphere centers. In the present paper, the existence of dual necklaces of $ k$ $ n$-dimensional cubes is discussed and the values of $ k$ are determined. A more general configuration of cubes, called a multidual necklace, is treated similarly.

References [Enhancements On Off] (What's this?)

  • [1] David Sanders, On extremal circuits, Doctoral Dissertation, City University of New York, 1968 (unpublished).

Additional Information

Keywords: Dual necklace, rectilinear circuit, $ n$-dimensional cube, multidual necklace, convex, centrally symmetric, $ 2n$-gon
Article copyright: © Copyright 1972 American Mathematical Society