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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Borsuk-Ulam theorem and bisection of necklaces


Authors: Noga Alon and Douglas B. West
Journal: Proc. Amer. Math. Soc. 98 (1986), 623-628
MSC: Primary 05A20; Secondary 05A15, 54H25, 55M20, 68R05
MathSciNet review: 861764
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Abstract: The Borsuk-Ulam theorem of topology is applied to a problem in discrete mathematics. A bisection of a necklace with $ k$ colors of beads is a collection of intervals whose union captures half the beads of each color. Every necklace with $ k$ colors has a bisection formed by at most $ k$ cuts. Higher-dimensional generalizations are considered.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0861764-9
PII: S 0002-9939(1986)0861764-9
Article copyright: © Copyright 1986 American Mathematical Society