{"title":"为类人猿的伯格曼粉丝提供最小的热带基地","authors":"Yasuhito Nakajima","doi":"10.21099/tkbjm/20234701019","DOIUrl":null,"url":null,"abstract":"The Bergman fan of a matroid is the intersection of tropical hyperplanes defined by the circuits. A tropical basis is a subset of the circuit set that defines the Bergman fan. Yu and Yuster posed a question whether every simple regular matroid has a unique minimal tropical basis of its Bergman fan, and verified it for graphic, cographic matroids and R10. We show every simple binary matroid has a unique minimal tropical basis. Since the regular matroid is binary, we positively answered the question.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.3000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"MINIMAL TROPICAL BASES FOR BERGMAN FANS OF MATROIDS\",\"authors\":\"Yasuhito Nakajima\",\"doi\":\"10.21099/tkbjm/20234701019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Bergman fan of a matroid is the intersection of tropical hyperplanes defined by the circuits. A tropical basis is a subset of the circuit set that defines the Bergman fan. Yu and Yuster posed a question whether every simple regular matroid has a unique minimal tropical basis of its Bergman fan, and verified it for graphic, cographic matroids and R10. We show every simple binary matroid has a unique minimal tropical basis. Since the regular matroid is binary, we positively answered the question.\",\"PeriodicalId\":44321,\"journal\":{\"name\":\"Tsukuba Journal of Mathematics\",\"volume\":\"47 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tsukuba Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21099/tkbjm/20234701019\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsukuba Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21099/tkbjm/20234701019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
MINIMAL TROPICAL BASES FOR BERGMAN FANS OF MATROIDS
The Bergman fan of a matroid is the intersection of tropical hyperplanes defined by the circuits. A tropical basis is a subset of the circuit set that defines the Bergman fan. Yu and Yuster posed a question whether every simple regular matroid has a unique minimal tropical basis of its Bergman fan, and verified it for graphic, cographic matroids and R10. We show every simple binary matroid has a unique minimal tropical basis. Since the regular matroid is binary, we positively answered the question.
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