| 书目名称 | Ordered Sets | | 副标题 | An Introduction | | 编辑 | Bernd S. W. Schröder | | 视频video | | | 图书封面 |  | | 描述 | .This work is an introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. ..A wide range of material is presented, from classical results such as Dilworth‘s, Szpilrajn‘s and Hashimoto‘s Theorems to more recent results such as the Li--Milner Structure Theorem. Major topics covered include: chains and antichains, lowest upper and greatest lower bounds, retractions, lattices, the dimension of ordered sets, interval orders, lexicographic sums, products, enumeration, algorithmic approaches and the role of algebraic topology. ..Since there are few prerequisites, the text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory class. After working through a comparatively lean core, the reader can choose from a diverse range of topics such as structure theory, enumeration or algorithmic aspects. Also presented are some | | 出版日期 | Textbook 20031st edition | | 关键词 | Algebraic topology; Arithmetic; Lattice; Lemma; calculus; combinatorics; discrete mathematics; graph theory | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-0053-6 | | isbn_softcover | 978-1-4612-6591-7 | | isbn_ebook | 978-1-4612-0053-6 | | copyright | Springer Science+Business Media New York 2003 |
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发表于 2025-3-21 16:35:31
