Karola M'esz'aros, Linus Setiabrata, Avery St. Dizier
{"title":"An orthodontia formula for Grothendieck polynomials","authors":"Karola M'esz'aros, Linus Setiabrata, Avery St. Dizier","doi":"10.1090/tran/8529","DOIUrl":null,"url":null,"abstract":"We give a new operator formula for Grothendieck polynomials that generalizes Magyar's Demazure operator formula for Schubert polynomials. Unlike the usual recursive definition of Grothendieck polynomials, the new formula is ascending in degree. Our proofs are purely combinatorial, contrasting with the geometric and representation theoretic tools used by Magyar for his operator formula for Schubert polynomials. Additionally, our approach yields a new proof of Magyar's formula.","PeriodicalId":8442,"journal":{"name":"arXiv: Combinatorics","volume":"62 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tran/8529","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We give a new operator formula for Grothendieck polynomials that generalizes Magyar's Demazure operator formula for Schubert polynomials. Unlike the usual recursive definition of Grothendieck polynomials, the new formula is ascending in degree. Our proofs are purely combinatorial, contrasting with the geometric and representation theoretic tools used by Magyar for his operator formula for Schubert polynomials. Additionally, our approach yields a new proof of Magyar's formula.