{"title":"The number of partial Steiner systems and d-partitions","authors":"R. Hofstad, R. Pendavingh, J. V. D. Pol","doi":"10.19086/aic.32563","DOIUrl":null,"url":null,"abstract":"We prove asymptotic upper bounds on the number of $d$-partitions (paving matroids of fixed rank) and partial Steiner systems (sparse paving matroids of fixed rank), using a mixture of entropy counting, sparse encoding, and the probabilistic method.","PeriodicalId":36338,"journal":{"name":"Advances in Combinatorics","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.19086/aic.32563","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1
Abstract
We prove asymptotic upper bounds on the number of $d$-partitions (paving matroids of fixed rank) and partial Steiner systems (sparse paving matroids of fixed rank), using a mixture of entropy counting, sparse encoding, and the probabilistic method.
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