Book Review
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3891927
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Book Information:
Editor:
Miklós Bóna
Title:
Handbook of enumerative combinatorics
Additional book information:
Discrete Mathematics and its Applications, edited by
Miklós Bóna,
CRC Press,
Boca Raton, FL,
2015,
xxiii+1061 pp.,
ISBN 978-1-4822-2085-8,
hardcover
M. F. Atiyah, R. Bott, and L. Gȧrding, Lacunas for hyperbolic differential operators with constant coefficients. I, Acta Math. 124 (1970), 109–189. MR 470499, DOI 10.1007/BF02394570
Julius Borcea and Petter Brändén, The Lee-Yang and Pólya-Schur programs. I. Linear operators preserving stability, Invent. Math. 177 (2009), no. 3, 541–569. MR 2534100, DOI 10.1007/s00222-009-0189-3
Julius Borcea and Petter Brändén, The Lee-Yang and Pólya-Schur programs. II. Theory of stable polynomials and applications, Comm. Pure Appl. Math. 62 (2009), no. 12, 1595–1631. MR 2569072, DOI 10.1002/cpa.20295
Julius Borcea, Petter Brändén, and Thomas M. Liggett, Negative dependence and the geometry of polynomials, J. Amer. Math. Soc. 22 (2009), no. 2, 521–567. MR 2476782, DOI 10.1090/S0894-0347-08-00618-8
C. Berge, Principles of combinatorics, Mathematics in Science and Engineering, Vol. 72, Academic Press, New York-London, 1971. Translated from the French. MR 0270922
James Haglund and Mirkó Visontai, On the monotone column permanent conjecture, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), Discrete Math. Theor. Comput. Sci. Proc., AK, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2009, pp. 443–454 (English, with English and French summaries). MR 2721533
R. P. Dilworth, Book Review: Matroid theory, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1353–1356. MR 1567099, DOI 10.1090/S0002-9904-1978-14577-7
G. P. Egorychev, The solution of van der Waerden’s problem for permanents, Adv. in Math. 42 (1981), no. 3, 299–305. MR 642395, DOI 10.1016/0001-8708(81)90044-X
D. I. Falikman, Proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix, Mat. Zametki 29 (1981), no. 6, 931–938, 957 (Russian). MR 625097
Philippe Flajolet and Andrew Odlyzko, Singularity analysis of generating functions, SIAM J. Discrete Math. 3 (1990), no. 2, 216–240. MR 1039294, DOI 10.1137/0403019
Philippe Flajolet and Robert Sedgewick, Analytic combinatorics, Cambridge University Press, Cambridge, 2009. MR 2483235, DOI 10.1017/CBO9780511801655
Sergey Fomin and Andrei Zelevinsky, Cluster algebras. I. Foundations, J. Amer. Math. Soc. 15 (2002), no. 2, 497–529. MR 1887642, DOI 10.1090/S0894-0347-01-00385-X
Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, Adv. in Appl. Math. 28 (2002), no. 2, 119–144. MR 1888840, DOI 10.1006/aama.2001.0770
Lars Gårding, Linear hyperbolic partial differential equations with constant coefficients, Acta Math. 85 (1951), 1–62. MR 41336, DOI 10.1007/BF02395740
I. P. Goulden and D. M. Jackson, Combinatorial enumeration, Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons, Inc., New York, 1983. With a foreword by Gian-Carlo Rota. MR 702512
Mark Goresky and Robert MacPherson, Stratified Morse theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 14, Springer-Verlag, Berlin, 1988. MR 932724, DOI 10.1007/978-3-642-71714-7
Shayan Oveis Gharan, Amin Saberi, and Mohit Singh, A randomized rounding approach to the traveling salesman problem, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science—FOCS 2011, IEEE Computer Soc., Los Alamitos, CA, 2011, pp. 550–559. MR 2932731, DOI 10.1109/FOCS.2011.80
Osman Güler, Hyperbolic polynomials and interior point methods for convex programming, Math. Oper. Res. 22 (1997), no. 2, 350–377. MR 1450796, DOI 10.1287/moor.22.2.350
André Joyal, Une théorie combinatoire des séries formelles, Adv. in Math. 42 (1981), no. 1, 1–82 (French, with English summary). MR 633783, DOI 10.1016/0001-8708(81)90052-9
László Lovász, Large networks and graph limits, American Mathematical Society Colloquium Publications, vol. 60, American Mathematical Society, Providence, RI, 2012. MR 3012035, DOI 10.1090/coll/060
I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1979. MR 553598
Grégory Miermont, The Brownian map is the scaling limit of uniform random plane quadrangulations, Acta Math. 210 (2013), no. 2, 319–401. MR 3070569, DOI 10.1007/s11511-013-0096-8
Adam W. Marcus, Daniel A. Spielman, and Nikhil Srivastava, Interlacing families II: Mixed characteristic polynomials and the Kadison-Singer problem, Ann. of Math. (2) 182 (2015), no. 1, 327–350. MR 3374963, DOI 10.4007/annals.2015.182.1.8
J. Nes̆etr̆il, Book review: Large netrworks and graph limits, Bull. Amer. Math. Soc., 51 (2014), 663–667.
Peter Orlik and Louis Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980), no. 2, 167–189. MR 558866, DOI 10.1007/BF01392549
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
Robin Pemantle, Hyperbolicity and stable polynomials in combinatorics and probability, Current developments in mathematics, 2011, Int. Press, Somerville, MA, 2012, pp. 57–123. MR 3098077
J. Schur and G. Pólya, Über zwei Arten von Faktorenfolgen in der Theorie der algebraischen Gleichungen, J. Reine Angew. Math. 144 (1914), 89–113 (German). MR 1580897, DOI 10.1515/crll.1914.144.89
Robin Pemantle and Mark C. Wilson, Analytic combinatorics in several variables, Cambridge Studies in Advanced Mathematics, vol. 140, Cambridge University Press, Cambridge, 2013. MR 3088495, DOI 10.1017/CBO9781139381864
Kyoji Saito, Theory of logarithmic differential forms and logarithmic vector fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), no. 2, 265–291. MR 586450
Richard P. Stanley, Book Review: Symmetric functions and Hall polynomials, Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 2, 254–265. MR 1567316, DOI 10.1090/S0273-0979-1981-14902-8
Richard P. Stanley, Enumerative combinatorics. Vol. 1, Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge, 1997. With a foreword by Gian-Carlo Rota; Corrected reprint of the 1986 original. MR 1442260, DOI 10.1017/CBO9780511805967
Hiroaki Terao, Arrangements of hyperplanes and their freeness. I, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), no. 2, 293–312. MR 586451
Terence Tao and Van H. Vu, Additive combinatorics, Cambridge Studies in Advanced Mathematics, vol. 105, Cambridge University Press, Cambridge, 2010. Paperback edition [of MR2289012]. MR 2573797
D. J. A. Welsh, Matroid theory, L. M. S. Monographs, No. 8, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976. MR 0427112
Herbert S. Wilf, generatingfunctionology, 2nd ed., Academic Press, Inc., Boston, MA, 1994. MR 1277813
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
References
- M. F. Atiyah, R. Bott, and L. Gårding, Lacunas for hyperbolic differential operators with constant coefficients. I, Acta Math. 124 (1970), 109–189. MR 0470499
- Julius Borcea and Petter Brändén, The Lee-Yang and Pólya-Schur programs. I. Linear operators preserving stability, Invent. Math. 177 (2009), no. 3, 541–569. MR 2534100
- Julius Borcea and Petter Brändén, The Lee-Yang and Pólya-Schur programs. II. Theory of stable polynomials and applications, Comm. Pure Appl. Math. 62 (2009), no. 12, 1595–1631. MR 2569072
- Julius Borcea, Petter Brändén, and Thomas M. Liggett, Negative dependence and the geometry of polynomials, J. Amer. Math. Soc. 22 (2009), no. 2, 521–567. MR 2476782
- C. Berge, Principles of combinatorics, Translated from the French. Mathematics in Science and Engineering, Vol. 72, Academic Press, New York-London, 1971. MR 0270922
- James Haglund and Mirkó Visontai, On the monotone column permanent conjecture, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), Discrete Math. Theor. Comput. Sci. Proc., AK, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2009, pp. 443–454 (English, with English and French summaries). MR 2721533
- R. P. Dilworth, Book review: Matroid theory, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1353–1356. MR 1567099
- G. P. Egorychev, The solution of van der Waerden’s problem for permanents, Adv. in Math. 42 (1981), no. 3, 299–305. MR 642395
- D. I. Falikman, Proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix, Mat. Zametki 29 (1981), no. 6, 931–938, 957 (Russian). MR 625097
- Philippe Flajolet and Andrew Odlyzko, Singularity analysis of generating functions, SIAM J. Discrete Math. 3 (1990), no. 2, 216–240. MR 1039294
- Philippe Flajolet and Robert Sedgewick, Analytic combinatorics, Cambridge University Press, Cambridge, 2009. MR 2483235
- Sergey Fomin and Andrei Zelevinsky, Cluster algebras. I. Foundations, J. Amer. Math. Soc. 15 (2002), no. 2, 497–529. MR 1887642
- Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, Adv. in Appl. Math. 28 (2002), no. 2, 119–144. MR 1888840
- Lars Gårding, Linear hyperbolic partial differential equations with constant coefficients, Acta Math. 85 (1951), 1–62. MR 0041336
- I. P. Goulden and D. M. Jackson, Combinatorial enumeration, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1983. With a foreword by Gian-Carlo Rota; Wiley-Interscience Series in Discrete Mathematics. MR 702512
- Mark Goresky and Robert MacPherson, Stratified Morse theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 14, Springer-Verlag, Berlin, 1988. MR 932724
- Shayan Oveis Gharan, Amin Saberi, and Mohit Singh, A randomized rounding approach to the traveling salesman problem, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science—FOCS 2011, IEEE Computer Soc., Los Alamitos, CA, 2011, pp. 550–559. MR 2932731
- Osman Güler, Hyperbolic polynomials and interior point methods for convex programming, Math. Oper. Res. 22 (1997), no. 2, 350–377. MR 1450796
- André Joyal, Une théorie combinatoire des séries formelles, Adv. in Math. 42 (1981), no. 1, 1–82 (French, with English summary). MR 633783
- László Lovász, Large networks and graph limits, American Mathematical Society Colloquium Publications, vol. 60, American Mathematical Society, Providence, RI, 2012. MR 3012035
- I. G. Macdonald, Symmetric functions and Hall polynomials, The Clarendon Press, Oxford University Press, New York, 1979. Oxford Mathematical Monographs. MR 553598
- Grégory Miermont, The Brownian map is the scaling limit of uniform random plane quadrangulations, Acta Math. 210 (2013), no. 2, 319–401. MR 3070569
- Adam W. Marcus, Daniel A. Spielman, and Nikhil Srivastava, Interlacing families II: Mixed characteristic polynomials and the Kadison-Singer problem, Ann. of Math. (2) 182 (2015), no. 1, 327–350. MR 3374963
- J. Nes̆etr̆il, Book review: Large netrworks and graph limits, Bull. Amer. Math. Soc., 51 (2014), 663–667.
- Peter Orlik and Louis Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980), no. 2, 167–189. MR 558866
- 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
- Robin Pemantle, Hyperbolicity and stable polynomials in combinatorics and probability, Current developments in mathematics, 2011, Int. Press, Somerville, MA, 2012, pp. 57–123. MR 3098077
- J. Schur and G. Pólya, Über zwei Arten von Faktorenfolgen in der Theorie der algebraischen Gleichungen, J. Reine Angew. Math. 144 (1914), 89–113 (German). MR 1580897
- Robin Pemantle and Mark C. Wilson, Analytic combinatorics in several variables, Cambridge Studies in Advanced Mathematics, vol. 140, Cambridge University Press, Cambridge, 2013. MR 3088495
- Kyoji Saito, Theory of logarithmic differential forms and logarithmic vector fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), no. 2, 265–291. MR 586450
- Richard P. Stanley, Book Review: Symmetric functions and Hall polynomials, Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 2, 254–265. MR 1567316
- Richard P. Stanley, Enumerative combinatorics. Vol. 1, Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge, 1997. With a foreword by Gian-Carlo Rota; Corrected reprint of the 1986 original. MR 1442260
- Hiroaki Terao, Arrangements of hyperplanes and their freeness. I, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), no. 2, 293–312. MR 586451
- Terence Tao and Van H. Vu, Additive combinatorics, Cambridge Studies in Advanced Mathematics, vol. 105, Cambridge University Press, Cambridge, 2010. Paperback edition [of MR2289012]. MR 2573797
- D. J. A. Welsh, Matroid theory, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976. L. M. S. Monographs, No. 8. MR 0427112
- Herbert S. Wilf, generatingfunctionology, 2nd ed., Academic Press, Inc., Boston, MA, 1994. MR 1277813
- 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
Review Information:
Reviewer:
Robin Pemantle
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Email:
pemantle@math.upenn.edu
Journal:
Bull. Amer. Math. Soc.
56 (2019), 159-164
DOI:
https://doi.org/10.1090/bull/1607
Published electronically:
December 14, 2017
Additional Notes:
Supported in part by NSF grant # DMS-1612674
Review copyright:
© Copyright 2017
American Mathematical Society
