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Abstract: Central and local limit theorems are derived for the number of distinct summands in integer partitions, with or without repetitions, under a general scheme essentially due to Meinardus. The local limit theorems are of the form of Cramer-type large deviations and are proved by Mellin transform and the two-dimensional saddle-point method. Applications of these results include partitions into positive integers, into powers of integers, into integers [j ], # > 1, into aj + b, etc. 1 (Update)
Context of citations to this paper: More
.... distinct summands in partitions were derived by Goh and Schmutz [21] see also Schmutz [45] Local limit theorems were studied by Hwang [26]. The corresponding problems for compositions are, unlike most other ones, more complicated and first treated by Knopfmacher and Mays [31,...
...are of the forms 1j k A 0 A ; and 0 1jk A 0 j k A ; 9 where k 1. It should be mentioned, as has been emphasized in [9], that if the multiplicity of each summand is counted only once, or if each part is allowed to appear at most once, then the limiting distributions of...
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6: On some problems of the statistical theory of partitions with application to cha.. (context) - Szalay, Tur'an - 1977
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BibTeX entry: (Update)
H.-K. Hwang. Limit theorems for the number of summands in integer partitions. submitted. http://citeseer.ist.psu.edu/article/hwang00limit.html More
@misc{ hwang-limit,
author = "H. Hwang",
title = "Limit theorems for the number of summands in integer partitions",
text = "H.-K. Hwang. Limit theorems for the number of summands in integer partitions.
submitted.",
url = "citeseer.ist.psu.edu/article/hwang00limit.html" }
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