Description
Time 10:15-11:00
Title: Bisecting and D-secting families for hypergraphs
Abstract: Let n be any positive integer, [n]:={1,2,...,n}, and suppose
$D\subset\{-n,-n+1,..,-1,0,1,...,n}$. Let F be a family of
subsets of [n]. A family F' of subsets of [n] is said to be
D-secting for F if for every A in the family F, there exists a subset A'
in F' such that $|A\cap A'|-|A\cap ([n]\setminus A')| = i$, for some $i\in
D$. A D-secting family F' of F, where D = {-1,0,1}, is a bisecting family
ensuring the existence of a subset $A'\in F'$ such that $|A\cap
A'|\in{\lfloor |A|/2\rfloor, \lceil |A|/2\rceil\}$ for each $A\in F$. We
consider the problem of determining minimal D-secting families F' for
certain families F and some related questions.
This is based on joint work with Rogers Mathew, Tapas Mishra, and
Sudebkumar Prashant Pal.