Book Review
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MathSciNet review:
3925371
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Book Information:
Authors:
Marcelo Aguiar and
Swapneel Mahajan
Title:
Topics in hyperplane arrangements
Additional book information:
Mathematical Surveys and Monographs, Vol. 226,
American Mathematical Society,
Providence, RI,
2017,
xxiv+611 pp.,
ISBN 978-1-4704-3711-4,
US$159.00
Review Information:
Reviewer:
S. Forcey
Affiliation:
Department of Mathematics, The University of Akron, Akron, Ohio
Email:
sf34@uakron.edu
Alissa S. Crans, Józef H. Przytycki, and Krzysztof K. Putyra, Torsion in one-term distributive homology, Fund. Math. 225 (2014), no. 1, 75–94. MR 3205566, DOI 10.4064/fm225-1-5
Alexandru Dimca, Hyperplane arrangements, Universitext, Springer, Cham, 2017. An introduction. MR 3618796, DOI 10.1007/978-3-319-56221-6
Martin Gardner, Wheels, life and other mathematical amusements, W. H. Freeman and Co., San Francisco, CA, 1983. MR 717760
Jacob E. Goodman and Joseph O’Rourke (eds.), Handbook of discrete and computational geometry, CRC Press Series on Discrete Mathematics and its Applications, CRC Press, Boca Raton, FL, 1997. MR 1730156
Branko Grünbaum, Convex polytopes, 2nd ed., Graduate Texts in Mathematics, vol. 221, Springer-Verlag, New York, 2003. Prepared and with a preface by Volker Kaibel, Victor Klee and Günter M. Ziegler. MR 1976856, DOI 10.1007/978-1-4613-0019-9
David Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982), no. 1, 37–65. MR 638121, DOI 10.1016/0022-4049(82)90077-9
F. William Lawvere, Linearization of graphic toposes via Coxeter groups, J. Pure Appl. Algebra 168 (2002), no. 2-3, 425–436. Category theory 1999 (Coimbra). MR 1887168, DOI 10.1016/S0022-4049(01)00107-4
Peter Orlik and Hiroaki Terao, Arrangements of hyperplanes, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 300, Springer-Verlag, Berlin, 1992. MR 1217488, DOI 10.1007/978-3-662-02772-1
Gian-Carlo Rota, Report on the present state of combinatorics, Proceedings of the 5th Conference on Formal Power Series and Algebraic Combinatorics (Florence, 1993), 1996, pp. 289–303. MR 1394961, DOI 10.1016/0012-365X(95)00143-K
Franco V. Saliola, The face semigroup algebra of a hyperplane arrangement, Canad. J. Math. 61 (2009), no. 4, 904–929. MR 2541389, DOI 10.4153/CJM-2009-046-2
Peter W. Shor, Stretchability of pseudolines is NP-hard, Applied geometry and discrete mathematics, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 4, Amer. Math. Soc., Providence, RI, 1991, pp. 531–554. MR 1116375
Neil J. A. Sloane, The on-line encyclopedia of integer sequences, Notices Amer. Math. Soc. 65 (2018), no. 9, 1062–1074. MR 3822822
Richard P. Stanley, Hyperplane arrangements, interval orders, and trees, Proc. Nat. Acad. Sci. U.S.A. 93 (1996), no. 6, 2620–2625. MR 1379568, DOI 10.1073/pnas.93.6.2620
Jacques Tits, Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics, Vol. 386, Springer-Verlag, Berlin-New York, 1974. MR 0470099
E. W. Weisstein, Kobon triangle, MathWorld—A Wolfram Web Resource, mathworld.wolfram.com/KobonTriangle.html (2018).
Thomas Zaslavsky, Facing up to arrangements: face-count formulas for partitions of space by hyperplanes, Mem. Amer. Math. Soc. 1 (1975), no. issue 1, 154, vii+102. MR 357135, DOI 10.1090/memo/0154
Günter M. Ziegler, Lectures on polytopes, Graduate Texts in Mathematics, vol. 152, Springer-Verlag, New York, 1995. MR 1311028, DOI 10.1007/978-1-4613-8431-1
References
- Alissa S. Crans, Józef H. Przytycki, and Krzysztof K. Putyra, Torsion in one-term distributive homology, Fund. Math. 225 (2014), no. 1, 75–94. MR 3205566, DOI 10.4064/fm225-1-5
- Alexandru Dimca, Hyperplane arrangements: An introduction, Universitext, Springer, Cham, 2017. MR 3618796, DOI 10.1007/978-3-319-56221-6
- Martin Gardner, Wheels, life and other mathematical amusements, W. H. Freeman and Co., San Francisco, CA, 1983. MR 717760
- Jacob E. Goodman and Joseph O’Rourke (eds.), Handbook of discrete and computational geometry, CRC Press Series on Discrete Mathematics and its Applications, CRC Press, Boca Raton, FL, 1997. MR 1730156
- Branko Grünbaum, Convex polytopes, 2nd ed., Graduate Texts in Mathematics, vol. 221, Springer-Verlag, New York, 2003. Prepared and with a preface by Volker Kaibel, Victor Klee and Günter M. Ziegler. MR 1976856, DOI 10.1007/978-1-4613-0019-9
- David Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Algebra 23 (1982), no. 1, 37–65. MR 638121, DOI 10.1016/0022-4049(82)90077-9
- F. William Lawvere, Linearization of graphic toposes via Coxeter groups, J. Pure Appl. Algebra 168 (2002), no. 2-3, 425–436. Category theory 1999 (Coimbra). MR 1887168, DOI 10.1016/S0022-4049(01)00107-4
- Peter Orlik and Hiroaki Terao, Arrangements of hyperplanes, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 300, Springer-Verlag, Berlin, 1992. MR 1217488, DOI 10.1007/978-3-662-02772-1
- Gian-Carlo Rota, Report on the present state of combinatorics, Proceedings of the 5th Conference on Formal Power Series and Algebraic Combinatorics (Florence, 1993), 1996, pp. 289–303. MR 1394961, DOI 10.1016/0012-365X(95)00143-K
- Franco V. Saliola, The face semigroup algebra of a hyperplane arrangement, Canad. J. Math. 61 (2009), no. 4, 904–929. MR 2541389, DOI 10.4153/CJM-2009-046-2
- Peter W. Shor, Stretchability of pseudolines is NP-hard, Applied geometry and discrete mathematics, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 4, Amer. Math. Soc., Providence, RI, 1991, pp. 531–554. MR 1116375
- Neil J. A. Sloane, The on-line encyclopedia of integer sequences, Notices Amer. Math. Soc. 65 (2018), no. 9, 1062–1074. MR 3822822
- Richard P. Stanley, Hyperplane arrangements, interval orders, and trees, Proc. Nat. Acad. Sci. U.S.A. 93 (1996), no. 6, 2620–2625. MR 1379568, DOI 10.1073/pnas.93.6.2620
- Jacques Tits, Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics, Vol. 386, Springer-Verlag, Berlin-New York, 1974. MR 0470099
- E. W. Weisstein, Kobon triangle, MathWorld—A Wolfram Web Resource, mathworld.wolfram.com/KobonTriangle.html (2018).
- Thomas Zaslavsky, Facing up to arrangements: face-count formulas for partitions of space by hyperplanes, Mem. Amer. Math. Soc. 1 (1975), no. issue 1, 154, vii+102. MR 0357135
- Günter M. Ziegler, Lectures on polytopes, Graduate Texts in Mathematics, vol. 152, Springer-Verlag, New York, 1995. MR 1311028, DOI 10.1007/978-1-4613-8431-1
Review Information:
Journal:
Bull. Amer. Math. Soc.
56 (2019), 367-372
DOI:
https://doi.org/10.1090/bull/1660
Published electronically:
December 12, 2018
Review copyright:
© Copyright 2018
American Mathematical Society