##### Department of Mathematics,

University of California San Diego

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### Food for Thought

## Morgan Makhina

#### UCSD

## From Spanning Trees to Permutation Factorizations

##### Abstract:

In this talk we will explore one useful connection between graphs and permutation groups. With a little help from A. Cayley we'll see how many spanning trees a graph with n vertices has. Then we'll use this to find the number of minimal-length factorizations of a permutation into transpositions. The material should be accessible to anyone with a rudimentary knowledge of group theory. Undergraduates welcome!

### November 27, 2023

### 1:00 PM

HSS 4025

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