The asymptotics of $e^{P\left ( z \right )}$ and the number of elements of each order in $S_n$
HTML articles powered by AMS MathViewer
- by Herbert S. Wilf PDF
- Bull. Amer. Math. Soc. 15 (1986), 228-232
References
- S. Chowla, I. N. Herstein, and W. K. Moore, On recursions connected with symmetric groups. I, Canad. J. Math. 3 (1951), 328–334. MR 41849, DOI 10.4153/cjm-1951-038-3
- S. Chowla, I. N. Herstein, and W. R. Scott, The solutions of $x^d=1$ in symmetric groups, Norske Vid. Selsk. Forh., Trondheim 25 (1952), 29–31 (1953). MR 0054605
- Ernst Jacobsthal, Sur le nombre d’éléments du groupe symétrique $S_n$ dont l’ordre est un nombre premier, Norske Vid. Selsk. Forh., Trondheim 21 (1949), no. 12, 49–51 (French). MR 0034761
- Leo Moser and Max Wyman, On solutions of $x^d=1$ in symmetric groups, Canadian J. Math. 7 (1955), 159–168. MR 68564, DOI 10.4153/CJM-1955-021-8
- Leo Moser and Max Wyman, Asymptotic expansions, Canadian J. Math. 8 (1956), 225–233. MR 78488, DOI 10.4153/CJM-1956-026-x
- W. K. Hayman, A generalisation of Stirling’s formula, J. Reine Angew. Math. 196 (1956), 67–95. MR 80749, DOI 10.1515/crll.1956.196.67
- Leo Moser and Max Wyman, Asymptotic expansions. II, Canadian J. Math. 9 (1957), 194–209. MR 86921, DOI 10.4153/CJM-1957-023-3
- Max Wyman, The asymptotic behaviour of the Laurent coefficients, Canadian J. Math. 11 (1959), 534–555. MR 107121, DOI 10.4153/CJM-1959-050-1 9. E. T. Whittaker and G. N. Watson, A course of modem analysis, 4th ed., Cambridge, 1958.
- Edward A. Bender, Asymptotic methods in enumeration, SIAM Rev. 16 (1974), 485–515. MR 376369, DOI 10.1137/1016082
- Bernard Harris and Lowell Schoenfeld, Asymptotic expansions for the coefficients of analytic functions, Illinois J. Math. 12 (1968), 264–277. MR 224801
- A. M. Odlyzko and L. B. Richmond, Asymptotic expansions for the coefficients of analytic generating functions, Aequationes Math. 28 (1985), no. 1-2, 50–63. MR 781207, DOI 10.1007/BF02189391
Additional Information
- Journal: Bull. Amer. Math. Soc. 15 (1986), 228-232
- MSC (1985): Primary 05A05, 05A15, 05A20, 10A50, 30D15, 41A60
- DOI: https://doi.org/10.1090/S0273-0979-1986-15486-8
- MathSciNet review: 854561