4th Algorithmic and Enumerative Combinatorics Summer School 2018 |

### Invited Speakers

- François Bergeron (Université du Québec à
Montréal, Canada)
**Combinatorial enumeration using symmetric functions, with computer algebra exploration**

Abstract: Symmetric functions provide one of the most efficient tools for combinatorial enumeration, in the context of objects that may be acted upon by permutations. Only assuming a basic knowledge of linear algebra, we will introduce and describe the toolbox of symmetric functions; and give many interesting examples of their uses. In particular, we will see that many classical formulas of enumerative combinatorics afford a natural generalization in terms of symmetric functions. This will come together with several proposed experimental explorations using computer algebra tools (using SageMath; or Maple, Mathematica, etc.). We will also mention some accessible open (but hard) problems, including some related to algebraic "versions" of P vs NP; as well as a few open problems that may be more manageable.Further information (including references and software preparation) can be found here .

- Éric Fusy (Laboratoire d'informatique de l'École polytechnique, France)
- George Labahn (University of Waterloo, Canada)