论文信息 - A new short proof of a theorem of Ahlswede and Khachatrian

A new short proof of a theorem of Ahlswede and Khachatrian

Ahlswede and Khachatrian [R. Ahlswede, L.H. Khachatrian, The complete nontrivial-intersection theorem for systems of finite sets, J. Combin. Theory Ser. A 76 (1996) 121-138] proved the following theorem, which answered a question of Frankl and Furedi [P. Frankl, Z. Furedi, Nontrivial intersecting families, J. Combin. Theory Ser. A 41 (1986) 150-153]. Let 2==(t+1)(k-t+1). Suppose that F is a family of k-subsets of an n-set, every two of which have at least t common elements. If |@?"F"@?"FF|

József Balogh | Dhruv Mubayi

[1] Zoltán Füredi,et al. Non-trivial intersecting families , 1986, J. Comb. Theory, Ser. A.

[2] Richard M. Wilson,et al. The exact bound in the Erdös-Ko-Rado theorem , 1984, Comb..

[3] A. J. W. Hilton,et al. SOME INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS , 1967 .

[4] P. Erdös,et al. INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS , 1961 .

[5] Rudolf Ahlswede,et al. The Complete Intersection Theorem for Systems of Finite Sets , 1997, Eur. J. Comb..

[6] Peter Frankl,et al. On intersecting families of finite sets , 1978, Bulletin of the Australian Mathematical Society.

[7] Rudolf Ahlswede,et al. The Complete Nontrivial-Intersection Theorem for Systems of Finite Sets , 1996, J. Comb. Theory, Ser. A.