Algebraic Representation of Topologies on a Finite Set

Autor:	Hongfeng Guo, Bing Xing, Ziwei Ming, Jun-E Feng
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	the number of topologies semi-tensor product structure matrices Mathematics QA1-939
Zdroj:	Mathematics, Vol 10, Iss 7, p 1143 (2022)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math10071143
Popis:	Since the 1930s, topological counting on finite sets has been an interesting work so as to enumerate the number of corresponding order relations on the sets. Starting from the semi-tensor product (STP), we give the expression of the relationship between subsets of finite sets from the perspective of algebra. Firstly, using the STP of matrices, we present the algebraic representation of the subset and complement of finite sets and corresponding structure matrices. Then, we investigate respectively the relationship between the intersection and union and intersection and minus of structure matrices. Finally, we provide an algorithm to enumerate the numbers of topologies on a finite set based on the above theorems.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/8f29ee677197414e8f44ee9f56855296 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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