##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Jeff Remmel

#### UCSD

## Frame patterns in $n$-cycles.

##### Abstract:

We study the generating function for the simplest frame pattern called the $\mu$-pattern in $n$-cycles. Given a cycle $C =(c_1, \ldots, c_n)$, we say that $(c_i,c_j)$ matches the $\mu$-pattern if $c_i < c_j$ and there is no $c_k$ which lies cyclicly between $c_i$ and $c_j$ such that $c_i < c_k < c_j$. We will show that the study of $\mu$-patterns in $n$-cycles give rise to a new $q$-analogue of the derangement numbers and has a rather surprising connection with the charge statistic of Lascoux and Schutzenberger.

### October 14, 2014

### 4:00 PM

### AP&M 7321

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