Michelle Wachs, University of Miami

Symmetric functions and Eulerian polynomials

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Left: random standard Young tableaux (using Dan Romik’s software), Right: Eulerian polynomials computed by Euler in 1755

Teaching Assistant: Rafael S. González D'León, University of Kentucky (USA)

List of topics

1. Permutation statistics and Eulerian polynomials. Lecture 1 notes Exercises Ejercicios

2. Symmetric and quasisymmetric functions. Lecture 2  notes Exercises Ejercicios

3. Eulerian quasisymmetric functions. Lecture 3 notes Exercises Ejercicios

4. Chromatic quasisymmetric functions. Lecture 4 notes Exercises Ejercicios

Main References

1. Shareshian, John; Wachs, Michelle L.; Eulerian quasisymmetric functions, Adv. Math. 225 (2010), no. 6, 2921–2966.

2. Shareshian, John; Wachs, Michelle L.; Chromatic quasisymmetric functions, Adv. Math. 295 (2016), 497–551.

3. Shareshian, John; Wachs, Michelle L.; From Poset Topology to q-Eulerian Polynomials to Stanley's Chromatic Symmetric Functions, Arxiv preprint  2016.  

4. Stanley, Richard P.; Enumerative Combinatorics Volume 1 Second edition,  Cambridge Studies in Advanced Mathematics 49, 2011.

5. Stanley, Richard P.; Enumerative Combinatorics Volume 2,  Cambridge Studies in Advanced Mathematics 62, 1999.