{"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}
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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].
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