Asymmetric function theory
arXiv:1904.01358 · doi:10.1007/978-981-15-7451-1_5
Abstract
The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to the larger ring of quasisymmetric functions, with corresponding applications. Here, we survey recent work extending this theory further to general asymmetric polynomials.
36 pages, 8 figures, 1 table. Written for the proceedings of the Schubert calculus conference in Guangzhou, Nov. 2017
References in corpus (6)
- A Decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth Algorithm
- Kohnert tableaux and a lifting of quasi-Schur functions
- Set-Valued Skyline Fillings
- Combinatorial models for Schubert polynomials
- The genomic Schur function is fundamental-positive
- Multiplication of a Schubert polynomial by a Stanley symmetric polynomial