{"title":"Simple geometric mitosis","authors":"Valentina Kiritchenko","doi":"10.1016/j.jcta.2025.106022","DOIUrl":null,"url":null,"abstract":"<div><div>We construct simple geometric operations on faces of the Cayley sum of two polytopes. These operations can be thought of as convex geometric counterparts of divided difference operators in Schubert calculus. We show that these operations give a uniform construction of Knutson–Miller mitosis in the type <em>A</em> and Fujita mitosis in the type <em>C</em> on Kogan faces of Gelfand–Zetlin polytopes.</div></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":"213 ","pages":"Article 106022"},"PeriodicalIF":1.2000,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series A","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0097316525000172","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/2/24 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We construct simple geometric operations on faces of the Cayley sum of two polytopes. These operations can be thought of as convex geometric counterparts of divided difference operators in Schubert calculus. We show that these operations give a uniform construction of Knutson–Miller mitosis in the type A and Fujita mitosis in the type C on Kogan faces of Gelfand–Zetlin polytopes.
期刊介绍：
The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.
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