摘要
设X为一个n元集合,Cnk为X的所有k元子集全体,若A∈A,B∈B有|A∩B|≥t,则称(A,B)为一个交叉t-相交子集族.本文得到最大交叉t-相交子集族和最大非空交叉2-相交子集族.证明如下两个结论.(1)若(A,B)为一个交叉t-相交子集族,且a≤b及a+b≤n+t-1,则|A+B|≤max{(bn),(an)},且当(A;B)=(φ,Cnb)或(Cna,φ)时达到上界.(2)若(A,B)为一个交叉2-相交子集族,且a<b,a+b≤n-1及(n,a,b)≠(2i,i-1,i)(i为任意正整数),又A,B均非空,则|A+B|≤1+(bn)-(b(n-a))-a((b-1)(n-a))且当(A,B)=({A},Cnb-{B||B|=b,|A∩B|≤1})时达到上界.
Let Cnk be the set of all k-subsets of an n-set. Assume A Cna and B Cnb.(A, B) is called a cross-t-intersecting family if |A ∩ B|≥t for any A ∈A, B ∈ B. In this paper, we obtain |A+ B| for maximum cross-t-intersecting families and maximum non-empty cross-2-intersecting families of subsets and show that either of the maximum bounds is best possible, namely, attainable by certain special cases.
出处
《数学进展》
CSCD
北大核心
1996年第3期210-216,共7页
Advances in Mathematics(China)
关键词
相交子集族
子集
交叉t-相交定理
intersecting
cross-t-intersecting
cross-2-intersecting