TY - JOUR
T1 - Splitting necklaces
AU - Alon, Noga
PY - 1987/3
Y1 - 1987/3
N2 - Let N be an opened necklace with kai beads of color i, 1 ≤ i ≤ t. We show that it is possible to cut N in (k - 1) · t places and partition the resulting intervals into k collections, each containing precisely ai beads of color i, 1 ≤ i ≤ t. This result is best possible and solves a problem of Goldberg and West. Its proof is topological and uses a generalization, due to Bárány, Shlosman and Szücs, of the Borsuk-Ulam theorem. By similar methods we obtain a generalization of a theorem of Hobby and Rice on L1-approximation.
AB - Let N be an opened necklace with kai beads of color i, 1 ≤ i ≤ t. We show that it is possible to cut N in (k - 1) · t places and partition the resulting intervals into k collections, each containing precisely ai beads of color i, 1 ≤ i ≤ t. This result is best possible and solves a problem of Goldberg and West. Its proof is topological and uses a generalization, due to Bárány, Shlosman and Szücs, of the Borsuk-Ulam theorem. By similar methods we obtain a generalization of a theorem of Hobby and Rice on L1-approximation.
UR - http://www.scopus.com/inward/record.url?scp=38249037947&partnerID=8YFLogxK
U2 - 10.1016/0001-8708(87)90055-7
DO - 10.1016/0001-8708(87)90055-7
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AN - SCOPUS:38249037947
SN - 0001-8708
VL - 63
SP - 247
EP - 253
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 3
ER -