##### Department of Mathematics,

University of California San Diego

****************************

### Math 264 - Combinatorics

## Sergey Kitaev

#### UCSD (Visiting Scholar)

## Introduction to partially ordered patterns

##### Abstract:

Is there any simple way to describe walks, starting from the origin, in the positive quadrant between lattice points, each in a direction N, S, E or W, in terms of pattern avoidance in permutations? Does there exist a pattern with the property that the number of $n$-permutations avoiding it equals the number of $n$-permutations having cycles of length at most $k$? To answer these questions and to provide other interesting facts, we introduce the concept of partially ordered patterns (POPs), which generalize the generalized patterns introduced by Babson and Steingrimsson in 2000. We also discuss some of the results on POPs in the literature and suggest few problems to solve.

Host:

### April 26, 2005

### 4:00 PM

### AP&M 7321

****************************