Document Zbl 0242.05006

Central and local limit theorems applied to asymptotic enumeration. (English) Zbl 0242.05006

J. Comb. Theory, Ser. A 15, 91-111 (1973).

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MSC:

05A15	Exact enumeration problems, generating functions
60F05	Central limit and other weak theorems

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[1]	Carlitz, L., Eulerian numbers and polynomials, Math. Mag., 32, 247-260 (1959) · Zbl 0092.06601
[2]	David, F. N.; Barton, E. E., Combinatorial Chance (1962), Griffin: Griffin London
[3]	Gnedenko, B. V.; Kolmogorov, A. N., Limit Distributions for Sums of Independent Random Variables (1954), Addison-Wesley: Addison-Wesley Cambridge, Mass, (trans. from Russian by K. L. Chung) · Zbl 0056.36001
[4]	Good, I. J., Saddle-point methods for the multinomial distribution, Ann. Math. Statist., 28, 861-881 (1957) · Zbl 0091.14302
[5]	Harper, L. H., Stirling behavior is asymptotically normal, Ann. Math. Statist., 38, 410-414 (1967) · Zbl 0154.43703
[6]	Lieb, E. H., Concavity properties and a generating function for Stirling numbers, J. Combinatorial Theory, 5, 203-206 (1968) · Zbl 0164.33002
[7]	McQuistan, R. B.; Lichtman, S. J., Exact recursion relation for 2 × \(N\) arrays of dumbbells, J. Math. Phys., 11, 3095-3099 (1970)
[8]	Moser, L.; Wyman, M., Asymptotic development of the Stirling numbers of the first kind, J. London Math. Soc., 33, 133-146 (1958) · Zbl 0081.28202
[9]	Moser, L.; Wyman, M., Stirling numbers of the second kind, Duke Math. J., 25, 29-48 (1958) · Zbl 0079.09102
[10]	Moskvin, D. A.; Postnikova, L. P.; Yudin, A. A., An arithmetic method for obtaining local limit theorems for lattice random variables, Theor. Probability Appl., 15, 87-97 (1970) · Zbl 0229.60020
[11]	Vervaat, W., Nieuw Arch. Wisk., 19, 3, 87 (1971), problem no. 258

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