{"title":"Möbius条的三角剖分数","authors":"Bazier-Matte Véronique, Huang Ruiyan, Luo Hanyi","doi":"10.2140/involve.2023.16.547","DOIUrl":null,"url":null,"abstract":"Consider a M\\\"obius strip with $n$ chosen points on its edge. A triangulation is a maximal collection of arcs among these points and cuts the strip into triangles. In this paper, we proved the number of all triangulations that one can obtain from a M\\\"obius strip with $n$ chosen points on its edge is given by $4^{n-1}+\\binom{2n-2}{n-1}$, then we made the connection with the number of clusters in the quasi-cluster algebra arising from the M\\\"obius strip.","PeriodicalId":36396,"journal":{"name":"Involve","volume":"16 9","pages":"0"},"PeriodicalIF":0.2000,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Number of triangulations of a Möbius strip\",\"authors\":\"Bazier-Matte Véronique, Huang Ruiyan, Luo Hanyi\",\"doi\":\"10.2140/involve.2023.16.547\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Consider a M\\\\\\\"obius strip with $n$ chosen points on its edge. A triangulation is a maximal collection of arcs among these points and cuts the strip into triangles. In this paper, we proved the number of all triangulations that one can obtain from a M\\\\\\\"obius strip with $n$ chosen points on its edge is given by $4^{n-1}+\\\\binom{2n-2}{n-1}$, then we made the connection with the number of clusters in the quasi-cluster algebra arising from the M\\\\\\\"obius strip.\",\"PeriodicalId\":36396,\"journal\":{\"name\":\"Involve\",\"volume\":\"16 9\",\"pages\":\"0\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2023-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Involve\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/involve.2023.16.547\",\"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":"Involve","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/involve.2023.16.547","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Consider a M\"obius strip with $n$ chosen points on its edge. A triangulation is a maximal collection of arcs among these points and cuts the strip into triangles. In this paper, we proved the number of all triangulations that one can obtain from a M\"obius strip with $n$ chosen points on its edge is given by $4^{n-1}+\binom{2n-2}{n-1}$, then we made the connection with the number of clusters in the quasi-cluster algebra arising from the M\"obius strip.
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