Grothendieck多项式的正畸公式

arXiv: Combinatorics Pub Date : 2020-11-27 DOI:10.1090/tran/8529

Karola M'esz'aros, Linus Setiabrata, Avery St. Dizier

{"title":"Grothendieck多项式的正畸公式","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":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"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\":null,\"pages\":null},\"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}","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

摘要

推广Magyar关于Schubert多项式的Demazure算子公式，给出了Grothendieck多项式的一个新的算子公式。与通常的格罗滕迪克多项式的递归定义不同，新公式的阶是升的。我们的证明是纯组合的，与Magyar为舒伯特多项式的算子公式使用的几何和表示理论工具形成对比。此外，我们的方法产生了马扎尔公式的新证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

An orthodontia formula for Grothendieck polynomials

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv: Combinatorics

自引率

0.00%

发文量