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Field name	Details
Dewey Class	511.6
Title	Greedoids ([EBook]) / by Bernhard Korte, Rainer Schrader, László Lovász.
Author	Korte, Bernhard H.
Added Personal Name	Schrader, Rainer
Added Personal Name	Lovász, László
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1991.
Physical Details	VIII, 214 pages : online resource.
Series	Algorithms and Combinatorics 0937-5511 ; ; 4
ISBN	9783642581915
Summary Note	With the advent of computers, algorithmic principles play an ever increasing role in mathematics. Algorithms have to exploit the structure of the underlying mathematical object, and properties exploited by algorithms are often closely tied to classical structural analysis in mathematics. This connection between algorithms and structure is in particular apparent in discrete mathematics, where proofs are often ...:
Contents note	I. Introduction -- 1. Set Systems and Languages -- 2. Graphs, Partially Ordered Sets and Lattices -- II. Abstract Linear Dependence — Matroids -- 1. Matroid Axiomatizations -- 2. Matroids and Optimization -- 3. Operations on Matroids -- 4. Submodular Functions and Polymatroids -- III. Abstract Convexity — Antimatroids -- 1. Convex Geometries and Shelling Processes -- 2. Examples of Antimatroids -- 3. Circuits and Paths -- 4. Helly’s Theorem and Relatives -- 5. Ramsey-type Results -- 6. Representations of Antimatroids -- IV. General Exchange Structures — Greedoids -- 1. Basic Facts -- 2. Examples of Greedoids -- V. Structural Properties -- 1. Rank Function -- 2. Closure Operators -- 3. Rank and Closure Feasibility -- 4. Minors and Extensions -- 5. Interval Greedoids -- VI. Further Structural Properties -- 1. Lattices Associated with Greedoids -- 2. Connectivity in Greedoids -- VII. Local Poset Greedoids -- 1. Polymatroid Greedoids -- 2. Local Properties of Local Poset Greedoids -- 3. Excluded Minors for Local Posets -- 4. Paths in Local Poset Greedoids -- 5. Excluded Minors for Undirected Branchings Greedoids -- VIII. Greedoids on Partially Ordered Sets -- 1. Supermatroids -- 2. Ordered Geometries -- 3. Characterization of Ordered Geometries -- 4. Minimal and Maximal Ordered Geometries -- IX. Intersection, Slimming and Trimming -- 1. Intersections of Greedoids and Antimatroids -- 2. The Meet of a Matroid and an Antimatroid -- 3. Balanced Interval Greedoids -- 4. Exchange Systems and Gauss Greedoids -- X. Transposition Greedoids -- 1. The Transposition Property -- 2. Applications of the Transposition Property -- 3. Simplicial Elimination -- XI. Optimization in Greedoids -- 1. General Objective Functions -- 2. Linear Functions -- 3. Polyhedral Descriptions -- 4. Transversals and Partial Transversals -- 5. Intersection of Supermatroids -- XII. Topological Results for Greedoids -- 1. A Brief Review of Topological Prerequisites -- 2. Shellability of Greedoids and the Partial Tutte Polynomial -- 3. Homotopy Properties of Greedoids -- References -- Notation Index -- Author Index -- Inclusion Chart (inside the back cover).
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-642-58191-5
Links to Related Works	Subject References: Combinatorial analysis . Combinatorics . Mathematics . Authors: author . Korte, Bernhard H. . Korte, Bernhard H. . Lovász, László . Schrader, Rainer . Corporate Authors: SpringerLink (Online service) . Series: Algorithms and Combinatorics . Classification: 511.6 .

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Greedoids

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