### 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.

Original language | English (US) |
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Pages (from-to) | 623-628 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 98 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1986 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Alon, N., & West, D. B. (1986). The Borsuk-Ulam theorem and bisection of necklaces.

*Proceedings of the American Mathematical Society*,*98*(4), 623-628. https://doi.org/10.1090/S0002-9939-1986-0861764-9