## Markov chains on Abelian groups provide constructions for the diamond problem

- Feb. 6, 2015
- 2:15 p.m.
- LeConte 312

## Abstract

The diamond conjecture asserts that a family F of subsets of an n-element set, such that no two elements of F have simultaneously a common subset and a common superset in F, cannot have many more elements than twice the number of [n/2]-element subsets of the n-element set.

Infinitely many different constructions are shown, each dense on 3 levels, and each has size about twice the middle level. Citing results about Markov chains on Abelian groups saves a lot of work.

Joint work with E. Czabarka, A. Dutle, T. Johnston.