Description
Abstract: Let {(A_i,B_i)\}_{i=1}^m be a set pair system. F\"uredi, Gy\’ arf\’ as and Kir\'aly called it 1-cross intersecting if the size of intersection of A_i and B_j is 1 when i and j are distinct, and 0 if i=j. They studied such systems and their generalizations, and in particular considered m(a,b,1), the maximum size of a 1-cross intersecting set pair system in which |A_i|<= a and |B_i|<= b for all i.
Answering one of their questions, Holzman recently proved that if a,b>= 2, then m(a,b,1)<= (29/30)((a+b) choose a). He also conjectured that the factor 29/30 in his bound can be replaced by 5/6. The goal of this talk is to sketch a proof of this conjectured bound.
This is joint work with Grace Mc.Court and Mina Nahvi.
The link to kombszem is
https://zoom.us/j/2961946869