Book Review
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MathSciNet review:
1568107
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Book Information:
Author:
James G. Oxley
Title:
Matroid theory
Additional book information:
Oxford University Press, London 1992, xi + 532 pp., US$79.00. ISBN 0-19-853563-5.
Martin Aigner, Combinatorial theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 234, Springer-Verlag, Berlin-New York, 1979. MR 542445
Garrett Birkhoff, Abstract Linear Dependence and Lattices, Amer. J. Math. 57 (1935), no. 4, 800–804. MR 1507113, DOI 10.2307/2371015
Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
Anders Björner, Michel Las Vergnas, Bernd Sturmfels, Neil White, and Günter M. Ziegler, Oriented matroids, Encyclopedia of Mathematics and its Applications, vol. 46, Cambridge University Press, Cambridge, 1993. MR 1226888
Joseph P. S. Kung, A source book in matroid theory, Birkhäuser Boston, Inc., Boston, MA, 1986. With a foreword by Gian-Carlo Rota. MR 890330, DOI 10.1007/978-1-4684-9199-9
Eugene L. Lawler, Combinatorial optimization: networks and matroids, Holt, Rinehart and Winston, New York-Montreal, Que.-London, 1976. MR 0439106
András Recski, Matroid theory and its applications in electric network theory and in statics, Algorithms and Combinatorics, vol. 6, Springer-Verlag, Berlin; Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest, 1989. MR 1027839, DOI 10.1007/978-3-662-22143-3
P. D. Seymour, Decomposition of regular matroids, J. Combin. Theory Ser. B 28 (1980), no. 3, 305–359. MR 579077, DOI 10.1016/0095-8956(80)90075-1
K. Truemper, Matroid decomposition, Academic Press, Inc., Boston, MA, 1992. MR 1170126
W. T. Tutte, A homotopy theorem for matroids. I, II, Trans. Amer. Math. Soc. 88 (1958), 144–174. MR 101526, DOI 10.1090/S0002-9947-1958-0101526-0
D. J. A. Welsh, Matroid theory, L. M. S. Monographs, No. 8, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976. MR 0427112
[12] N. White, ed., Theory of matroids, Cambridge Univ. Press, Cambridge, 1986.
[13] -, Combinatorial geometries, Cambridge Univ. Press, Cambridge, 1987.
[14] -, Matroid applications, Cambridge Univ. Press, Cambridge, 1992.
Hassler Whitney, On the Abstract Properties of Linear Dependence, Amer. J. Math. 57 (1935), no. 3, 509–533. MR 1507091, DOI 10.2307/2371182
- [1]
- M. Aigner, Combinatorial theory, Springer-Verlag, Berlin, 1979. MR 542445 (80h:05002)
- [2]
- G. Birkhoff, Abstract linear dependence in lattices, Amer. J. Math. 57 (1935), 800-804. MR 1507113
- [3]
- -, Lattice theory, third ed., Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc, Providence, RI, 1967. MR 0227053 (37:2638)
- [4]
- A. Björner, M. Las Vergnas, B. Sturmfels, N. White, and G. Ziegler, Oriented matroids, Cambridge Univ. Press, Cambridge, 1993. MR 1226888 (95e:52023)
- [5]
- J. P. S. Kung, A source book in matroid theory, Birkhäuser, Boston, 1986. MR 890330 (88e:05028)
- [6]
- E. Lawler, Combinatorial optimization: networks and matroids, Holt, New York, 1976. MR 0439106 (55:12005)
- [7]
- A. Recski, Matroid theory and its applications in electrical network theory and in statics, Springer-Verlag, Berlin, 1989. MR 1027839 (91f:05038)
- [8]
- P. D. Seymour, Decomposition of regular matroids, J. Combin. Theory Ser. B 28 (1980), 305-359. MR 579077 (82j:05046)
- [9]
- K. Truemper, Matroid decomposition, Academic Press, Boston, 1992. MR 1170126 (93h:05046)
- [10]
- W. T. Tutte, A homotopy theorem for matroids. I, II, Trans. Amer. Math. Soc. 88 (1958), 144-174. MR 0101526 (21:336)
- [11]
- D. J. A. Welsh, Matroid theory, Academic Press, London, 1976. MR 0427112 (55:148)
- [12]
- N. White, ed., Theory of matroids, Cambridge Univ. Press, Cambridge, 1986.
- [13]
- -, Combinatorial geometries, Cambridge Univ. Press, Cambridge, 1987.
- [14]
- -, Matroid applications, Cambridge Univ. Press, Cambridge, 1992.
- [15]
- H. Whitney, On the abstract properties of linear dependence, Amer. J. Math. 57 (1935), 509-533. MR 1507091
Review Information:
Reviewer:
Neil L. White
Journal:
Bull. Amer. Math. Soc.
30 (1994), 252-254
DOI:
https://doi.org/10.1090/S0273-0979-1994-00457-4