{"title":"关联三角形对角线的比较","authors":"Samson Saneblidze, Ronald Umble","doi":"10.4310/hha.2024.v26.n1.a9","DOIUrl":null,"url":null,"abstract":"We prove that the formula for the diagonal approximation $\\Delta_K$ on J. Stasheff’s $n$-dimensional associahedron $K_{n+2}$ derived by the current authors in $\\href{ https://dx.doi.org/10.4310/HHA.2004.v6.n1.a20}{[7]}$ agrees with the “magical formula” for the diagonal approximation $\\Delta^\\prime_K$ derived by Markl and Shnider in $\\href{ https://www.ams.org/journals/tran/2006-358-06/S0002-9947-05-04006-7/ }{[5]}$, by J.-L. Loday in $\\href{ https://doi.org/10.1007/978-0-8176-4735-3_13 }{[4]}$, and more recently by Masuda, Thomas, Tonks, and Vallette in $\\href{ https://doi.org/10.5802/jep.142}{[6]}$.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Comparing diagonals on the associahedra\",\"authors\":\"Samson Saneblidze, Ronald Umble\",\"doi\":\"10.4310/hha.2024.v26.n1.a9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the formula for the diagonal approximation $\\\\Delta_K$ on J. Stasheff’s $n$-dimensional associahedron $K_{n+2}$ derived by the current authors in $\\\\href{ https://dx.doi.org/10.4310/HHA.2004.v6.n1.a20}{[7]}$ agrees with the “magical formula” for the diagonal approximation $\\\\Delta^\\\\prime_K$ derived by Markl and Shnider in $\\\\href{ https://www.ams.org/journals/tran/2006-358-06/S0002-9947-05-04006-7/ }{[5]}$, by J.-L. Loday in $\\\\href{ https://doi.org/10.1007/978-0-8176-4735-3_13 }{[4]}$, and more recently by Masuda, Thomas, Tonks, and Vallette in $\\\\href{ https://doi.org/10.5802/jep.142}{[6]}$.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/hha.2024.v26.n1.a9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/hha.2024.v26.n1.a9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove that the formula for the diagonal approximation $\Delta_K$ on J. Stasheff’s $n$-dimensional associahedron $K_{n+2}$ derived by the current authors in $\href{ https://dx.doi.org/10.4310/HHA.2004.v6.n1.a20}{[7]}$ agrees with the “magical formula” for the diagonal approximation $\Delta^\prime_K$ derived by Markl and Shnider in $\href{ https://www.ams.org/journals/tran/2006-358-06/S0002-9947-05-04006-7/ }{[5]}$, by J.-L. Loday in $\href{ https://doi.org/10.1007/978-0-8176-4735-3_13 }{[4]}$, and more recently by Masuda, Thomas, Tonks, and Vallette in $\href{ https://doi.org/10.5802/jep.142}{[6]}$.
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