Book Review
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MathSciNet review:
1567551
Full text of review:
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Book Information:
Authors:
Ian P. Goulden and
David M. Jackson
Title:
Combinatorial enumeration
Additional book information:
John Wiley & Sons, Inc., Somerset, New Jersey, 1983, xxiv + 569 pp., $47.50. ISBN 0-4718-6654-7.
1. D. André, Développement de sec x et de tang x, C. R. Acad. Sci. Paris 88 (1879), 965-967.
Edward A. Bender and Jay R. Goldman, Enumerative uses of generating functions, Indiana Univ. Math. J. 20 (1970/71), 753–765. MR 270931, DOI 10.1512/iumj.1971.20.20060
Louis Comtet, Advanced combinatorics, Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht, 1974. The art of finite and infinite expansions. MR 0460128
Peter Doubilet, Gian-Carlo Rota, and Richard Stanley, On the foundations of combinatorial theory. VI. The idea of generating function, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971) Univ. California Press, Berkeley, Calif., 1972, pp. 267–318. MR 0403987
P. Flajolet, Combinatorial aspects of continued fractions, Discrete Math. 32 (1980), no. 2, 125–161. MR 592851, DOI 10.1016/0012-365X(80)90050-3
Dominique Foata, La série génératrice exponentielle dans les problèmes d’énumération, Séminaire de Mathématiques Supérieures, No. 54 (Été, vol. 1971, Les Presses de l’Université de Montréal, Montreal, Que., 1974 (French). Avec un chapitre sur les identités probabilistes dérivées de la formule exponentielle, par B. Kittel. MR 0505546
Dominique Foata and Marcel-P. Schützenberger, Théorie géométrique des polynômes eulériens, Lecture Notes in Mathematics, Vol. 138, Springer-Verlag, Berlin-New York, 1970 (French). MR 0272642
Ira M. Gessel, A factorization for formal Laurent series and lattice path enumeration, J. Combin. Theory Ser. A 28 (1980), no. 3, 321–337. MR 570213, DOI 10.1016/0097-3165(80)90074-6
Ira Gessel, A noncommutative generalization and $q$-analog of the Lagrange inversion formula, Trans. Amer. Math. Soc. 257 (1980), no. 2, 455–482. MR 552269, DOI 10.1090/S0002-9947-1980-0552269-2
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
11. P. A. MacMahon, Second memoir on the composition of numbers, Phil. Trans. Roy. Soc. London Ser. A 207 (1908), 65-134.
R. J. Riddell Jr. and G. E. Uhlenbeck, On the theory of the virial development of the equation of state of mono-atomic gases, J. Chem. Phys. 21 (1953), 2056–2064. MR 59207, DOI 10.1063/1.1698742
Gian-Carlo Rota, On the foundations of combinatorial theory. I. Theory of Möbius functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2 (1964), 340–368 (1964). MR 174487, DOI 10.1007/BF00531932
Richard P. Stanley, Binomial posets, Möbius inversion, and permutation enumeration, J. Combinatorial Theory Ser. A 20 (1976), no. 3, 336–356. MR 409206, DOI 10.1016/0097-3165(76)90028-5
- 1.
- D. André, Développement de sec x et de tang x, C. R. Acad. Sci. Paris 88 (1879), 965-967.
- 2.
- E. A. Bender and J. R. Goldman, Enumerative uses of generating functions, Indiana Univ. Math. J. 20 (1971), 753-765. MR 0270931
- 3.
- L. Comtet, Advanced combinatorics, Reidel, Dordrecht, 1974. MR 460128
- 4.
- P. Doubilet, G.-C. Rota and R. Stanley, On the foundations of combinatorial theory. VI: The idea of generating function, Proc. Sixth Berkeley Sympos. Mathematical Statistics and Probability, Univ. of California Press, Berkeley, 1972, pp. 267-318. MR 403987
- 5.
- P. Flajolet, Combinatorial aspects of continued fractions, Discrete Math. 32 (1980), 125-161. MR 592851
- 6.
- D. Foata, La série génératrice exponentielle dans les problèmes d'énumeration, Les Presses de l'Université de Montréal, 1974. MR 505546
- 7.
- D. Foata and M.-P. Schützenberger, Théorie géometrique des polynômes eulériens, Lecture Notes in Math., vol. 138, Springer-Verlag, Berlin, 1970. MR 272642
- 8.
- I. M. Gessel, A factorization for formal Laurent series and lattice path enumeration, J. Combin. Theory Ser. A 28 (1980), 321-337. MR 570213
- 9.
- I. M. Gessel, A noncommutative generalization and q-analog of the Lagrange inversion formula, Trans. Amer. Math. Soc. 257 (1980), 455-481. MR 552269
- 10.
- A. Joyal, Une théorie combinatoire des séries formelles, Adv. in Math. 42 (1981), 1-82. MR 633783
- 11.
- P. A. MacMahon, Second memoir on the composition of numbers, Phil. Trans. Roy. Soc. London Ser. A 207 (1908), 65-134.
- 12.
- R. J. Riddell, Jr. and G. E. Uhlenbeck, On the theory of the virial development of the equation of state of monoatomic gases, J. Chem. Phys. 21 (1953), 2056-2064. MR 59207
- 13.
- G.-C. Rota, On the foundations of combinatorial theory. I: Theory of Möbius functions, Z. Wahrsch. Verw. Gebiete 2 (1964), 340-368. MR 174487
- 14.
- R. P. Stanley, Binomial posets, Möbius inversion, and permutation enumeration, J. Combin. Theory Ser. A 20 (1976), 336-356. MR 409206
Review Information:
Reviewer:
Ira Gessel
Journal:
Bull. Amer. Math. Soc.
12 (1985), 297-301
DOI:
https://doi.org/10.1090/S0273-0979-1985-15385-6
