The Borsuk-Ulam theorem and bisection of necklaces

Noga Alon; Douglas B. West

doi:10.1090/S0002-9939-1986-0861764-9

The Borsuk-Ulam theorem and bisection of necklaces

Noga Alon, Douglas B. West

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

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)
Pages (from-to)	623-628
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	98
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-1986-0861764-9
State	Published - Dec 1986
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9939-1986-0861764-9

Cite this

@article{07b75ebab29647578ba29429128e970c,

title = "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.",

author = "Noga Alon and West, {Douglas B.}",

year = "1986",

month = dec,

doi = "10.1090/S0002-9939-1986-0861764-9",

language = "English (US)",

volume = "98",

pages = "623--628",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "4",

}

TY - JOUR

T1 - The Borsuk-Ulam theorem and bisection of necklaces

AU - Alon, Noga

AU - West, Douglas B.

PY - 1986/12

Y1 - 1986/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000176239&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000176239&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1986-0861764-9

DO - 10.1090/S0002-9939-1986-0861764-9

M3 - Article

AN - SCOPUS:0000176239

SN - 0002-9939

VL - 98

SP - 623

EP - 628

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

The Borsuk-Ulam theorem and bisection of necklaces

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this