{"title":"组合为条形图","authors":"T. Mansour, A. S. Shabani","doi":"10.47443/dml.2022.0002","DOIUrl":null,"url":null,"abstract":"In this paper, we consider statistics on combinations of [n] when combinations are presented as bargraphs. The statistics we consider are cardinality of a combination, semi-perimeter, outer site-perimeter, and inner site-perimeter. We find an explicit formula for the generating function for the number of combinations of [n] according to the considered statistics. We also find an explicit formula for the total of the above statistics over all combinations of [n].","PeriodicalId":36023,"journal":{"name":"Discrete Mathematics Letters","volume":"1 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Combinations as Bargraphs\",\"authors\":\"T. Mansour, A. S. Shabani\",\"doi\":\"10.47443/dml.2022.0002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider statistics on combinations of [n] when combinations are presented as bargraphs. The statistics we consider are cardinality of a combination, semi-perimeter, outer site-perimeter, and inner site-perimeter. We find an explicit formula for the generating function for the number of combinations of [n] according to the considered statistics. We also find an explicit formula for the total of the above statistics over all combinations of [n].\",\"PeriodicalId\":36023,\"journal\":{\"name\":\"Discrete Mathematics Letters\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2022-02-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.47443/dml.2022.0002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/dml.2022.0002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we consider statistics on combinations of [n] when combinations are presented as bargraphs. The statistics we consider are cardinality of a combination, semi-perimeter, outer site-perimeter, and inner site-perimeter. We find an explicit formula for the generating function for the number of combinations of [n] according to the considered statistics. We also find an explicit formula for the total of the above statistics over all combinations of [n].
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