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 Lascoux-Schützenberger 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/virtual-permutations 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 1480.05137Marberg, Eric; Zhang, Yifeng 2022 Affine transitions for involution Stanley symmetric functions. Zbl 1435.05210Marberg, 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 (05-XX) 2 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) Citations by Year