Representation of Integer Positive Number as A Sum of Natural Summands
نویسندگان
چکیده
منابع مشابه
Distribution of integer partitions with large number of summands
The factor c−1 √ n log n is nothing but the asymptotic value of the mean number of summands in a random partition of n, each partition of n being equally likely; cf. [17]. Note that the number of partitions of n with m 1’s is given by p(n −m) − p(n −m − 1) for 0 ≤ m ≤ n; and, consequently, p(n−m) is nothing but the number of partitions of n which have ≥ m 1’s. Thus the factor one plays an impor...
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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 Cramér-type large deviations and are proved by Mellin transform and the two-dimensional saddle-point method. Applications of these results include partitions into posi...
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ژورنال
عنوان ژورنال: International Journal of Engineering Research and Applications
سال: 2017
ISSN: 2248-9622,2248-9622
DOI: 10.9790/9622-0706040108