{"title":"A variant of some cyclotomic matrices involving trinomial coefficients","authors":"Yu-Bo Li, Ning-Liu Wei","doi":"10.4064/cm9115-6-2023","DOIUrl":"https://doi.org/10.4064/cm9115-6-2023","url":null,"abstract":"By using the theory of circulant matrices we study some matrices over finite fields which involve the quadratic character and trinomial coefficients.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135440779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Amenability constants of central Fourier algebras of finite groups","authors":"John Sawatzky","doi":"10.4064/cm9018-9-2023","DOIUrl":"https://doi.org/10.4064/cm9018-9-2023","url":null,"abstract":"We consider amenability constants of the central Fourier algebra $ZA(G)$ of a finite group $G$. This is a dual object to $ZL^1(G)$ in the sense of hypergroup algebras, and as such shares similar amenability theory. We provide several classes of groups whe","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135446669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A factorization of metric spaces","authors":"Yoshito Ishiki","doi":"10.4064/cm9066-6-2023","DOIUrl":"https://doi.org/10.4064/cm9066-6-2023","url":null,"abstract":"We first prove that for every metrizable space $X$, for every closed subset $Fhphantom{i}$ whose complement is zero-dimensional, the space $X$ can be embedded as a closed subset into a product of the closed subset $F$ and a metrizable zero-dimensional sp","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A new proof of Stanley’s theorem on the strong Lefschetz property","authors":"Hong Phuong, Quang Hoa Tran","doi":"10.4064/cm8987-11-2022","DOIUrl":"https://doi.org/10.4064/cm8987-11-2022","url":null,"abstract":". A standard graded artinian monomial complete intersection algebra A = k [ x 1 , x 2 , . . . , x n ] / ( x a 1 1 , x a 2 2 , . . . , x a n n ), with k a field of characteristic zero, has the strong Lefschetz property due to Stanley in 1980. In this paper, we give a new proof for this result by using only the basic properties of linear algebra. Furthermore, our proof is still true in the case where the characteristic of k is greater than the socle degree of A , namely a 1 + a 2 + · · · + a n − n .","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49656153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asymptotic smoothness and universality\u0000in Banach spaces","authors":"R. Causey, G. Lancien","doi":"10.4064/cm8923-12-2022","DOIUrl":"https://doi.org/10.4064/cm8923-12-2022","url":null,"abstract":"For $1<pleqslant infty$, we study the complexity and the existence of universal spaces for two classes of separable Banach spaces, denoted $textsf{A}_p$ and $textsf{N}_p$, and related to asymptotic smoothness in Banach spaces. We show that each of these classes is Borel in the class of separable Banach spaces. Then we build small families of Banach spaces that are both injectively and surjectively universal for these classes. Finally, we prove the optimality of this universality result, by proving in particular that none of these classes admits a universal space.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43811983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}