##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Mike Hansen

#### UCSD

## SAGE and Symmetric Functions

##### Abstract:

SAGE is a free, open-source computer algebra that aims to be a replacement for Mathematica, Maple, Matlab, and Magma and was started by William Stein, a number theorist at the University of Washington. Recently, a lot of support has been added to SAGE for working with combinatorial objects such as partitions, permutations, tableaux, etc. Additionally, SAGE now has fairly good support for symmetric functions, which are "polynomials" in infinitely many variables which are invariant under any permutation of those variables. In this talk, I will give a brief introduction to SAGE and give an overview of symmetric functions and how to work with them in SAGE. I will also talk briefly about some generalizations of symmetric functions including Hall-Littlewood polynomials and Macdonald polynomials.

### November 13, 2007

### 3:00 PM

### AP&M 7321

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