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  1. Home
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  3. Matroids: A Geometric Introduction
  • Cited by 15
Publisher:
Cambridge University Press
Online publication date:
November 2012
Print publication year:
2012
Online ISBN:
9781139049443
DOI:
https://doi.org/10.1017/CBO9781139049443
Subjects:
Mathematics, Discrete Mathematics Information Theory and Coding, Geometry and Topology
Information

Book description

Matroid theory is a vibrant area of research that provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the geometric approach to matroids. Written in a friendly, fun-to-read style and developed from the authors' own undergraduate courses, the book is ideal for students. Beginning with a basic introduction to matroids, the book quickly familiarizes the reader with the breadth of the subject, and specific examples are used to illustrate the theory and to help students see matroids as more than just generalizations of graphs. Over 300 exercises are included, with many hints and solutions so students can test their understanding of the materials covered. The authors have also included several projects and open-ended research problems for independent study.

Reviews

"The authors write in an entertaining, conversational style, and the text is often peppered with humorous footnotes. Nearly 300 exercises and scores of references will benefit motivated readers."
-J. T. Saccoman, Choice

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Contents

Contents
References
Bibliography
Bibliography
[1] K., Appel and W., Haken. Every planar map is four colorable. Bull. Amer. Math. Soc., 82: 711–712, 1976.
[2] L., Babai, C., Pomerance and P., Vèrtesi. The mathematics of Paul Erdös. Notices of the AMS, 45(1): 19–31, 1998.
[3] G., Birkhoff. Abstract linear dependence in lattices. Amer. J. Math, 57: 800–804, 1935.
[4] G., Birkhoff. Lattice Theory, third edition, volume XXV. American Mathematical Society, Providence, RI, 1967.
[5] R., Bixby. On Reid's characterization of the ternary matroids. J. Combin. Theory Ser. B, 26: 174–204, 1979.
[6] A., Björner, M., Las Vergnas, B., Sturmfels, N., White and G., Ziegler. Oriented Matroids, Encyclopedia of Mathematics and Its Applications, volume 46. Cambridge, New York, 1993.
[7] A., Bondy and U. S. R., Murty. Graph Theory (Graduate Texts in Mathematics), volume 244. Springer, New York, 2008.
[8] T., Brylawski. A decomposition for combinatorial geometries. Trans. Amer. Math. Soc., 171: 235–282, 1972.
[9] T., Brylawski. Appendix of matroid cryptomorphisms. Encyclopedia Math. Appl. – Theory of Matroids, 26(1): 298–312, 1986.
[10] T., Brylawski and D., Kelly. Matroids and Combinatorial Geometries, Carolina Lecture Series, volume 8. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 1980.
[11] T., Brylawski and J., Oxley. The Tutte polynomial and its applications. Encyclopedia Math. Appl. – Matroid Applications, 40: 123–225, 1992.
[12] H., Crapo. The Tutte polynomial. Aequationes Math., 3: 211–229, 1969.
[13] P., Davis and R., Hersh. The Mathematical Experience. Birkhäuser, Boston, 1981.
[14] J., Geelen, A., Gerards and A., Kapoor. The excluded minors for GF(4)-representable matroids. J. Combin. Theory Ser. B, 79: 247–299, 2000.
[15] R., Graham and P., Hell. On the history of the minimum spanning tree problem. IEEE Ann. Hist. Comput., 7: 43–57, 1985.
[16] R. L., Graham, M., Grötschel and L., Lovász, editors. Handbook of Combinatorics, volume 1. Elsevier, Amsterdam, 1995.
[17] D., Hughes and F., Piper. Projective Planes, Graduate Texts in Mathematics, volume 6. Springer, New York, 1973.
[18] A. W., Ingleton. A note on independence functions and rank. J. London Math. Soc., 34: 4–56, 1959.
[19] D., Kelly and G.-C., Rota. Some problems in combinatorial geometry. Proc. Internat. Sympos., Colorado State Univ., Fort Collins, Colo., 1971, 57: 309–312, 1973.
[20] J., Kruskal. On the shortest spanning tree of a graph and the traveling salesman problem. Proc. Amer. Math. Soc., 7: 48–50, 1956.
[21] C. W. H., Lam, L., Thiel and S., Swiercz. The non-existence of finite projective planers of order 10. Canad. J. Math., XLI: 1117–1123, 1989.
[22] J., Lipton. An Exaltation of Larks. Penguin Books, New York, 1968, 1977, 1991.
[23] S., MacLane. Some interpretations of abstract linear dependence in terms of projective geometry. Amer. J. Math, 58: 236–240, 1936.
[24] C., Merino, A., de Mier and M., Noy. Irreducibility of the Tutte polynomial of a connected matroid. J. Combin. Theory Ser. B, 83: 298–304, 2001.
[25] J., Oxley. What is a matroid?Cubo Math. Educ., 5(3): 179–218, 2003.
[26] J., Oxley. Matroid Theory, second edition. Oxford University Press, New York, 2011.
[27] R., Rado. A theorem on independence relations. Quart. J. Math, 13: 83–89, 1942.
[28] N., Robertson, D., Sanders, P., Seymour and R., Thomas. A new proof of the four-colour theorem. Electron. Res. Announc. Amer. Math. Soc., 2: 17–25, 1996.
[29] G. C., Rota. On the foundations of combinatorial theory 1. Theory of Möbius functions. Z. Wahrscheinlichkeits theorie u. Verw. Gebiete, 2: 340–368, 1964.
[30] W., Schwärzler. Being Hamiltonian is not a Tutte invariant. Discrete Math., 91: 87–89, 1991.
[31] P., Seymour. Matroid representation over GF(3). J. Combin. Theory Ser. B, 26: 159–173, 1979.
[32] R., Stanley. An Introduction to Hyperplane Arrangements, IAS/Park City Mathematical Series, volume 14. American Mathematical Society, Providence, RI, 2004.
[33] R. P., Stanley. Acyclic orientations of graphs. Discrete Math., 5: 17–178, 1973.
[34] F., Stevenson. Projective Planes. Freeman, San Francisco, 1972.
[35] W. T., Tutte. A homotopy theorem for matroids I, II. Trans. Amer. Math. Soc., 88: 144–174, 1958.
[36] J. H., van Lint and R. M., Wilson. A Course in Combinatorics. Cambridge University Press, Cambridge, 1992.
[37] D. J. A., Welsh. Matroid Theory. L. M. S. Monographs, volume 8. Academic Press, London, 1976.
[38] D., West. Introduction to Graph Theory, second edition. Prentice Hall, 2001.
[39] N., White. Theory of Matroids, Encyclopedia of Mathematics and Its Applications, volume 26. Cambridge University Press, New York, 1986.
[40] N., White. Combinatorial Geometries, Encyclopedia of Mathematics and Its Applications, volume 29. Cambridge University Press, New York, 1987.
[41] N., White. Matroid Applications, Encyclopedia of Mathematics and Its Applications, volume 40. Cambridge University Press, New York, 1992.
[42] H., Whitney. On the abstract properties of linear dependence. Amer. J. Math, 57: 509–533, 1935.
[43] T., Zaslavsky. Facing up to Arrangements: Facecount Formulas for Partitions of Space by Hyperplanes, volume 154. American Mathematical Society, 1975.
[44] G., Ziegler. Lectures on Polytopes, Graduate Texts in Mathematics, volume 152. Springer, New York, 1995.

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