Virtual Permutations
swMATH ID:  40990 
Software Authors:  Marberg, Eric; Zhang, Yifeng 
Description:  Affine transitions for involution Stanley symmetric functions. We study a family of symmetric functions F indexed by involutions z in the affine symmetric group. These power series are analogues of Lam’s affine Stanley symmetric functions and generalizations of the involution Stanley symmetric functions introduced by Hamaker, Pawlowski, and the first author. Our main result is to prove a transition formula for F which can be used to define an affine involution analogue of the LascouxSchützenberger tree. Our proof of this formula relies on Lam and Shimozono’s transition formula for affine Stanley symmetric functions and some new technical properties of the strong Bruhat order on affine permutations. 
Homepage:  https://arxiv.org/abs/1812.04880 
Source Code:  https://github.com/emarberg/virtualpermutations 
Dependencies:  Python 
Related Software:  GitHub 
Cited in:  5 Publications 
Standard Articles
2 Publications describing the Software, including 2 Publications in zbMATH  Year 

Affine transitions for involution Stanley symmetric functions. Zbl 1480.05137 Marberg, Eric; Zhang, Yifeng 
2022

Affine transitions for involution Stanley symmetric functions. Zbl 1435.05210 Marberg, Eric; Zhang, Yifeng 
2019

Cited by 3 Authors
4  Marberg, Eric 
3  Zhang, Yifeng 
1  Pawlowski, Brendan Alexander 
Cited in 5 Serials
1  Journal of Algebra 
1  Journal of Pure and Applied Algebra 
1  European Journal of Combinatorics 
1  Selecta Mathematica. New Series 
1  Séminaire Lotharingien de Combinatoire 
Cited in 5 Fields
5  Combinatorics (05XX) 
2  Algebraic geometry (14XX) 
1  Associative rings and algebras (16XX) 
1  Nonassociative rings and algebras (17XX) 
1  Group theory and generalizations (20XX) 