عنوان

Matroids :

(Number (ISBN

0521145686

(Number (ISBN

0521767245

(Number (ISBN

9780521145688

(Number (ISBN

9780521767248

Number

dltt

Title Proper

Matroids :

General Material Designation

[Book]

Other Title Information

a geometric introduction /

First Statement of Responsibility

Gary Gordon, Jennifer McNulty

Specific Material Designation and Extent of Item

xv, 393 pages :

Other Physical Details

illustrations ;

Dimensions

26 cm

Text of Note

Includes bibliographical references and index

Text of Note

1. A tour of matroids -- 1.1. Motivation -- 1.2. Introduction to matroids -- 1.3. Geometries -- 1.4. Graphs and matroids -- 1.5. Bipartite graphs and transversal matroids -- Exercises -- 2. Cryptomorphisms -- 2.1. From independent sets to bases and back again -- 2.2. Circuits and independent sets -- 2.3. Rank, flats, hyperplanes and closure -- 2.4. Lattice of flats -- 2.5. Tying it together with the rank function -- 2.6. Cryptomorphisms between flats, hyperplanes and closure -- 2.7. Application to optimization: the greedy algorithm -- Exercises -- 3. New matroids from old -- 3.1. Matroid deletion and contraction -- 3.2. Deletion and contraction in graphs and representable matroids -- 3.3. Duality in matroids -- 3.4. Duality in graphic and representable matroids -- 3.5. Direct sums and connectivity -- Exercises -- 4. Graphic matroids -- 4.1. Graphs are matroids -- 4.2. Graph versions of matroid theorems -- 4.3. Duality and cocircuits in graphs -- 4.4. Connectivity and 2-isomorphism -- Exercises -- 5. Finite geometry -- 5.1. Affine geometry and affine dependence -- 5.2. Affine dependence -- 5.3. The projective plane PG(2, q) -- 5.4. Projective geometry -- 5.5. Counting k-flats and q-binomial coefficients -- 5.6. Abstract projective planes -- Exercises -- 6. Representable matroids -- 6.1. Matrices are matroids -- 6.2. Representing representable matroids -- 6.3. How representations depend on the field -- 6.4. Non-representable matroids -- 6.5. Representations and geometry -- Exercises -- 7. Other matroids -- 7.1. Transversal matroids -- 7.2. Transversal matroids, matching theory and geometry -- 7.3. Hyperplane arrangements and matroids -- 7.4. Cutting cheese; counting regions via deletion and contraction -- Exercises -- 8. Matroid minors -- 8.1. Examples, excluded minors and the Scum Theorem --8.2. Binary matroids -- 8.3. Summary of excluded minor results -- Exercises -- 9. The Tutte polynomial -- 9.1. Motivation and history -- 9.2. Definition and basic examples -- 9.3. Corank--nullity polynomial -- 9.4. Duality and direct sum -- 9.5. Tutte--Grothendieck invariants -- 9.6. The chromatic polynomial -- Exercises -- Projects -- P.1. The number of matroids -- P.2. Matrix-Tree Theorem -- P.3. Relaxing a hyperplane -- P.4. Bases and probability in affine and projective space -- P.5. Representing affine space -- the characteristic set of AG(n, q) -- P.6. The card game SET® and affine geometry -- P.7. More matroid constructions -- truncation -- Appendix Matroid axiom systems -- A.1. Axiom lists -- A.2. Axiom tables

0

Combinatorial geometry

Matroids

Class number

Book number

Gordon, Gary,1956-

McNulty, Jennifer

Date of Transaction

20131030112118.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y