Cutsets in the Boolean and Linear Lattices

10/05/2010 - 12:15pm
10/05/2010 - 1:10pm
Shahriar Shahriari (Pomona College)

In a partially ordered set a cutset is a collection of elements that intersects every maximal chain. If the elements of the poset where relay stations in a phone network and you could send a message from x to y if x was covered by y (that is, x < y and there doesn't exist a z with x< z < y), then a cutset would be a collection of relay stations whose malfunction would disconnect the set of minimal elements from the set of maximal elements. In this talk we focus on cutsets in the Boolean Lattices (subsets of a finite set ordered by inclusion) and in the Linear Lattices (subspaces of a finite dimensional vector space over a finite field). Some old results as well as some new results (in collaboration with the Spring 2010 undergraduate Research Circle at Pomona) will be presented.

Millikan 208 (Pomona College)