TY - JOUR

T1 - String Quartets in Binary

AU - Alon, Noga

AU - Körner, János

AU - Monti, Angelo

PY - 2000

Y1 - 2000

N2 - Let M(n, A) denote the maximum possible cardinality of a family of binary strings of length n, such that for every four distinct members of the family there is a coordinate in which exactly two of them have a 1. We prove that M(n,A) ≤ 20.78n for all sufficiently large n. Let M(n, C) denote the maximum possible cardinality of a family of binary strings of length n, such that for every four distinct members of the family there is a coordinate in which exactly one of them has a 1. We show that there is an absolute constant c < 1/2 such that M(n, C) ≤ 2cn for all sufficiently large n. Some related questions are discussed as well.

AB - Let M(n, A) denote the maximum possible cardinality of a family of binary strings of length n, such that for every four distinct members of the family there is a coordinate in which exactly two of them have a 1. We prove that M(n,A) ≤ 20.78n for all sufficiently large n. Let M(n, C) denote the maximum possible cardinality of a family of binary strings of length n, such that for every four distinct members of the family there is a coordinate in which exactly one of them has a 1. We show that there is an absolute constant c < 1/2 such that M(n, C) ≤ 2cn for all sufficiently large n. Some related questions are discussed as well.

UR - http://www.scopus.com/inward/record.url?scp=0442280202&partnerID=8YFLogxK

U2 - 10.1017/S0963548300004375

DO - 10.1017/S0963548300004375

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AN - SCOPUS:0442280202

SN - 0963-5483

VL - 9

SP - 381

EP - 390

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

IS - 5

ER -