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|a (Sirsi) i9780521767248
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|a 511/.6
|2 23
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|a Gordon, Gary,
|d 1956-
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|a Matroids :
|b a geometric introduction /
|c Gary Gordon, Jennifer McNulty.
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|a Cambridge ;
|a New York :
|b Cambridge University Press,
|c 2012.
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| 300 |
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|a xv, 393 páginas :
|b ilustraciones ;
|c 26 cm.
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|a Incluye bibliografías.
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|a 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{reg} and affine geometry -- P.7. More matroid constructions -- truncation -- Appendix Matroid axiom systems -- A.1. Axiom lists -- A.2. Axiom tables.
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|a Matroides.
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|a Geometría combinatoria.
|9 355529
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|a McNulty, Jennifer.
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