# Enumerative Combinatorics

Given a class of objects, one simple question one can ask is: how many are there? Sometimes this question may be easy to answer: there are
^{(n2-n)/2} graphs on

Usually in the process of enumerating a class of objects (whether exactly or asymptotically) one discovers that a typical object from the given class has certain properties (for example, a typical triangle-free graph is bipartite). This forms the basis for the study of random objects drawn from the class.

## Sample publications:

- D. Christofides. Induced lines in Hales-Jewett cubes
*Journal of Combinatorial Theory A*, 114: 906 - 918, 2007.

- P. Allen, V.V. Lozin and M. Rao. Clique-width and the speed of hereditary properties
*Electronic Journal of Combinatorics*, 16(1): R35, 2009.

- P. Allen. Forbidden induced bipartite graphs
*Journal of Graph Theory*, 60: 219 - 241, 2009.

- P. Allen. Almost every
2-SAT function is unate. *Israel Journal of Mathematics*, 161: 311 - 346, 2007.