Introduction to Matroids 1 Grzegorz
نویسندگان
چکیده
A subset family structure is a topological structure. LetM be a subset family structure and let A be a subset ofM . We introduce A is independent as a synonym of A is open. We introduce A is dependent as an antonym of A is open. Let M be a subset family structure. The family of M yielding a family of subsets of M is defined as follows: (Def. 1) The family of M = the topology of M . Let M be a subset family structure and let A be a subset of M . Let us observe that A is independent if and only if: (Def. 2) A ∈ the family of M . Let M be a subset family structure. We say that M is subset-closed if and only if: (Def. 3) The family of M is subset-closed.
منابع مشابه
An Introduction to Transversal Matroids
1. Prefatory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Several Perspectives on Transversal Matroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1. Set systems, transversals, partial transversals, and Hall’s theorem . . . . . . . . 2 2.2. Transversal matroids via matrix encodings of set systems . . . . . ....
متن کاملIntroduction to Combinatorial Optimization in Matroids
1. Matroids and Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 2. Greedy Algorithm and Matroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 3. Duality, Minors and Constructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کاملCATEGORICAL RELATIONS AMONG MATROIDS, FUZZY MATROIDS AND FUZZIFYING MATROIDS
The aim of this paper is to study the categorical relations betweenmatroids, Goetschel-Voxman’s fuzzy matroids and Shi’s fuzzifying matroids.It is shown that the category of fuzzifying matroids is isomorphic to that ofclosed fuzzy matroids and the latter is concretely coreflective in the categoryof fuzzy matroids. The category of matroids can be embedded in that offuzzifying matroids as a simul...
متن کاملWhat is a matroid? Theory and Applications, from the ground up
Gian-Carlo Rota said that “Anyone who has worked with matroids has come away with the conviction that matroids are one of the richest and most useful ideas of our day.” [20] Hassler Whitney introduced the theory of matroids in 1935 and developed a striking number of their basic properties as well as different ways to formulate the notion of a matroid. As more and more connections between matroi...
متن کاملAn Introduction to Extremal Matroid Theory with an Emphasis on the Geometric Perspective
1. The Scope of These Talks 1 2. Matroid Theory Background 2 2.1. Basic Concepts 3 2.2. New Matroids from Old 13 2.3. Representations of Matroids over Fields 18 2.4. Projective and Affine Geometries 23 3. A First Taste of Extremal Matroid Theory: Cographic Matroids 25 4. Excluding Subgeometries: The Bose-Burton Theorem 28 5. Excluding the (q + 2)-Point Line as a Minor 43 6. Excluding F7 as a Mi...
متن کامل