The symmetric functions catalog

An overview of symmetric functions and related topics

2022-10-20

Topics related to symmetric functions

Here is an overview of various topics which are related to symmetric functions, but do not fit together with a specific family. Some of the pages give 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!

Software resources

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.

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

References