The Borsuk-Ulam theorem and bisection of necklaces

Author:

Alon Noga,West Douglas B.

Abstract

The Borsuk-Ulam theorem of topology is applied to a problem in discrete mathematics. A bisection of a necklace with k k colors of beads is a collection of intervals whose union captures half the beads of each color. Every necklace with k k colors has a bisection formed by at most k k cuts. Higher-dimensional generalizations are considered.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference8 articles.

1. S. N. Bhatt and C. E. Leiserson, How to assemble tree machines, Proc. 14th ACM Sympos. Theor. Computing, San Francisco, Assoc. Comp. Mach., 1981, pp. 99-104.

2. K. Borsuk, Drei Satze uber die 𝑛-dimensionale euklidische Sphare, Fund, Math. 20 (1933), 177-190.

3. Bisection of circle colorings;Goldberg, Charles H.;SIAM J. Algebraic Discrete Methods,1985

4. A moment problem in 𝐿₁ approximation;Hobby, Charles R.;Proc. Amer. Math. Soc.,1965

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