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Báo cáo toán học: "The asymptotic number of set partitions with unequal block sizes"

Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài: The asymptotic number of set partitions with unequal block sizes. | The asymptotic number of set partitions with unequal block sizes A. Knopfmacher Department of Computational and Applied Mathematics University of Witwatersrand Johannesburg South Africa e-mail arnoldk@gauss.cam.wits.ac.za A. M. Odlyzko AT T Labs - Research Florham Park New Jersey 07932 USA e-mail amo@research.att.com B. Pittel1 Department of Mathematics Ohio State University Columbus Ohio 43210 USA e-mail bgp@math.ohio-state.edu L. B. Richmond Department of Combinatorics and Optimization University of Waterloo Waterloo Ontario N2L 3G1 Canada e-mail lbrichmo@watdragon.uwaterloo.ca D. Stark2 Department of Mathematics and Statistics University of Melbourne Parkville Victoria 3052 Australia e-mail dstark@maths.mu.oz.au G. Szekeres Department of Mathematics University of New South Wales Kensington New South Wales 2033 Australia e-mail G.Szekeres@unsw.edu.au N. C. Wormald3 Department of Mathematics and Statistics University of Melbourne Parkville Victoria 3052 Australia e-mail nick@maths.mu.oz.au Submitted April 20 1998 Accepted October 21 1998. 1 Research supported by the Focus on Discrete Probability Program at the Dimacs Center of Rutgers University in Spring of 1997 and under NSA Grant MDA 904-96-1-0053. 2Current address BRIMS Hewlett-Packard Labs Filton Road Stoke Gifford Bristol Bs12 6QZ UK 3Research supported by Australian Research Council THE ELECTRONIC JOURNAL OF COMBINATORICS 6 1999 R2 1 Abstract The asymptotic behavior of the number of set partitions of an n-element set into blocks of distinct sizes is determined. This behavior is more complicated than is typical for set partition problems. Although there is a simple generating function the usual analytic methods for estimating coefficients fail in the direct approach and elementary approaches combined with some analytic methods are used to obtain most of the results. Simultaneously we obtain results on the shape of a random partition of an n-element set into blocks of distinct sizes. Mathematics Subject .