{"title":"Elements of Calculus","authors":"A. Alenitsyn, E. Butikov, A. Kondratyev","doi":"10.1201/9781003068785-6","DOIUrl":"https://doi.org/10.1201/9781003068785-6","url":null,"abstract":"","PeriodicalId":124220,"journal":{"name":"Concise Handbook of Mathematics and Physics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127176311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Geometry. Stereometry","authors":"A. Alenitsyn, E. Butikov, A. Kondratyev","doi":"10.1201/9781003068785-10","DOIUrl":"https://doi.org/10.1201/9781003068785-10","url":null,"abstract":"","PeriodicalId":124220,"journal":{"name":"Concise Handbook of Mathematics and Physics","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131801946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sets. Real Numbers. Functions","authors":"A. Alenitsyn, E. Butikov, A. Kondratyev","doi":"10.1201/9781003068785-3","DOIUrl":"https://doi.org/10.1201/9781003068785-3","url":null,"abstract":"","PeriodicalId":124220,"journal":{"name":"Concise Handbook of Mathematics and Physics","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133987470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Basic Notations, Formulas, and Concepts","authors":"A. Alenitsyn, E. Butikov, A. Kondratyev","doi":"10.1201/9781003068785-2","DOIUrl":"https://doi.org/10.1201/9781003068785-2","url":null,"abstract":"","PeriodicalId":124220,"journal":{"name":"Concise Handbook of Mathematics and Physics","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132180747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Electricity and Magnetism","authors":"A. Alenitsyn, E. Butikov, A. Kondratyev","doi":"10.1201/9781003068785-17","DOIUrl":"https://doi.org/10.1201/9781003068785-17","url":null,"abstract":"","PeriodicalId":124220,"journal":{"name":"Concise Handbook of Mathematics and Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129001245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Combinatorics","authors":"A. Alenitsyn, Eugene I. Butikov, A. Kondratyev","doi":"10.1142/9789811202582_0002","DOIUrl":"https://doi.org/10.1142/9789811202582_0002","url":null,"abstract":". This is the first contribution of a sequence of papers introducing the notions of s -weak order and s -permutahedra, certain discrete objects that are indexed by a sequence of non-negative integers s . In this first paper, we concentrate purely on the combinatorics and lattice structure of the s -weak order, a partial order on certain decreasing trees which generalizes the classical weak order on permutations. In particular, we show that the s -weak order is a semidistributive and congruence uniform lattice, generalizing known results for the classical weak order on permutations. Restricting the s -weak order to certain trees gives rise to the s -Tamari lattice, a sublattice which generalizes the classical Tamari lattice. We show that the s -Tamari lattice can be obtained as a quotient lattice of the s -weak order when s has no zeros, and show that the s -Tamari lattices (for arbitrary s ) are isomorphic to the ν -Tamari lattices of Pr´eville-Ratelle and Viennot. The underlying geometric structure of the s -weak order will be studied in a sequel of this paper, where we introduce the notion of s -permutahedra.","PeriodicalId":124220,"journal":{"name":"Concise Handbook of Mathematics and Physics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131555334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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