TY - JOUR
T1 - AK-type stability theorems on cross t-intersecting families
AU - Lee, Sang June
AU - Siggers, Mark
AU - Tokushige, Norihide
N1 - Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2019/12
Y1 - 2019/12
N2 - Two families, A and B, of subsets of [n] are cross t-intersecting if for every A∈A and B∈B, A and B intersect in at least t elements. For a real number p and a family A the product measure μp(A) is defined as the sum of p|A|(1−p)n−|A| over all A∈A. For every non-negative integer r, and for large enough t, we determine, for any p satisfying [Formula presented] ≤p≤ [Formula presented], the maximum possible value of μp(A)μp(B) for cross t-intersecting families A and B. In this paper we prove a stronger stability result which yields the above result.
AB - Two families, A and B, of subsets of [n] are cross t-intersecting if for every A∈A and B∈B, A and B intersect in at least t elements. For a real number p and a family A the product measure μp(A) is defined as the sum of p|A|(1−p)n−|A| over all A∈A. For every non-negative integer r, and for large enough t, we determine, for any p satisfying [Formula presented] ≤p≤ [Formula presented], the maximum possible value of μp(A)μp(B) for cross t-intersecting families A and B. In this paper we prove a stronger stability result which yields the above result.
UR - http://www.scopus.com/inward/record.url?scp=85069725809&partnerID=8YFLogxK
U2 - 10.1016/j.ejc.2019.07.004
DO - 10.1016/j.ejc.2019.07.004
M3 - Article
AN - SCOPUS:85069725809
SN - 0195-6698
VL - 82
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
M1 - 102993
ER -