##### Department of Mathematics,

University of California San Diego

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### Special Combinatorics Seminar

## Mahir Can

#### Tulane University

## Enumeration in the rook monoid.

##### Abstract:

The rook monoid $R_n$ is the semigroup of 0/1 matrices of size n with at most one 1 in each row and column. The subgroup of invertible elements of $R_n$ is the symmetric group, and almost all questions about permutations make sense for the rooks. In this talk, without assuming any background in the subject, we 1. review some semigroup theoretic properties of $R_n$, 2. briefly explain the role of $R_n$ in the theory of algebraic monoids, 3. present some recent combinatorial results on $R_n$. In particular, we show that the celebrated numbers of mathematics such as Eulerian numbers, Catalan numbers, Stirling numbers, etc., all appear rather naturally in enumeration in $R_n$.

Host: Jeff Remmel

### February 12, 2010

### 1:00 PM

### AP&M 7218

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