The Borsuk-Ulam Theorem and Bisection of Necklaces

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. Higherdimensional generalizations are considered. © 1986 American Mathematical Society.