{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/affine-transitions-for-involution-stanley","title":"Affine transitions for involution Stanley symmetric functions","arxiv_id":"1812.04880","date":"2018-12-12","proceeding":null,"authors":["Eric Marberg","Yifeng Zhang"],"abstract":"We study a family of symmetric functions $\\hat F_z$ 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 $\\hat F_z$ which can be used to define an affine involution analogue of the Lascoux-Sch\\\"utzenberger 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.","url_abs":"https://arxiv.org/abs/1812.04880v4","url_pdf":"https://arxiv.org/pdf/1812.04880v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"affine-transitions-for-involution-stanley","repo_url":"https://github.com/emarberg/virtual-permutations","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}