The symmetric functions catalog

An overview of symmetric functions and related topics

2021-09-21

Topics related to symmetric functions

Here is an overview of various topics that are related to symmetric functions, but do not fit together with a specific family. Some of the pages gives a brief overview of the definitions and notation that is used.

We suggest that the reader is somewhat familiar with algebraic combinatorics, although a few topics is covered under preliminaries below. Furthermore, if you are a PhD student or researcher interested in symmetric functions, join our Facebook group!

These files are rather old — I intend to update them some time in the future, when the catalog include most of the quasisymmetric families.

Useful links

Suggested books

For an introduction to the topic of symmetric functions and algebraic combinatorics, I suggest the following books. Richard Stanley, Enumerative Combinatorics II [Sta01], Lynne Butler, Subgroup Lattices and Symmetric Functions [But94], Bruce Sagan, The Symmetric Group [Sag01], William Fulton, Young Tableaux [Ful97] and Ian Macdonald, Symmetric functions and Hall polynomials [Mac95].

Other related books: David Bressoud, Proofs and confirmations: the story of the alternating sign matrix conjecture [Bre99], which is a very nice reading.

References