منابع مشابه
Partitions into Primes
We investigate the asymptotic behavior of the partition function pΛ(n) defined by ∑∞ n=0 pΛ(n)x n = ∏∞ m=1(1−x), where Λ(n) denotes the von Mangoldt function. Improving a result of Richmond, we show that log pΛ(n) = 2 √ ζ(2)n+O( √ n exp{−c(logn)(log2 n)(log3 n)−1/3}), where c is a positive constant and logk denotes the k times iterated logarithm. We also show that the error term can be improved...
متن کاملGenerating Primes Using Partitions
This paper presents a new technique of generating large prime numbers using a smaller one by employing Goldbach partitions. Experiments are presented showing how this method produces candidate prime numbers that are subsequently tested using either Miller Rabin or AKS primality tests. Introduction Generation of large prime numbers is fundamental to modern cryptography protocols [1],[2], generat...
متن کاملPartitions Into
§1 . Asymptotic estimates for the number of partitions of the integer n into summands chosen from an arithmetic progression have been derived by several authors, see for example Meinardus [3] . In this note we investigate a natural extension which has not previosusly appeared in the literature . We shall study the asymptotic behaviour of the numbers p a a (n) and q (n), the number of partitions...
متن کاملPartitions into three triangular numbers
A celebrated result of Gauss states that every positive integer can be represented as the sum of three triangular numbers. In this article we study p3∆(n), the number of partitions of the integer n into three triangular numbers, as well as p3∆(n), the number of partitions of n into three distinct triangular numbers. Unlike t(n), which counts the number of representations of n into three triangu...
متن کاملPartitions of Graphs into Trees
In this paper, we study the k-tree partition problem which is a partition of the set of edges of a graph into k edge-disjoint trees. This problem occurs at several places with applications e.g. in network reliability and graph theory. In graph drawing there is the still unbeaten (n − 2) × (n − 2) area planar straight line drawing of maximal planar graphs using Schnyder’s realizers [15], which a...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2000
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-00-02386-2