H.-K. Hwang, Limit theorems for the number of summands in integer partitions, submitted. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Distribution of Integer Partitions With Large Number of Summands - Hwang (1997) (3 citations) (Correct)
....being more complicated. The method used here is also suitable for the quantities studied by Szalay and Turan in [22, 23] The generating functions there are of the forms # 1#j k # # # # 1#j#k # # # j k 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 the number of summands are Gaussian for a large class of partitions. For more quantitative results, see [9] General combinatorial inequalities for ....
....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 the number of summands are Gaussian for a large class of partitions. For more quantitative results, see [9]. General combinatorial inequalities for p # (n, m) are developed in [11] which are especially useful for partitions with a small number of summands. Appendix. In this appendix, we sketch the proof of (11) details can be found in [9] In Meinardus s original paper, the error term for p # (n) in ....
[Article contains additional citation context not shown here]
H.-K. Hwang, Limit theorems for the number of summands in integer partitions, submitted.
Distribution of Integer Partitions With Large Number of Summands - Hwang (1997) (3 citations) (Correct)
....complicated. The method used here is also suitable for the quantities studied by Szalay and Tur an in [22, 23] The generating functions there 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 the number of summands are Gaussian for a large class of partitions. For more quantitative results, see [9] General combinatorial inequalities ....
....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 the number of summands are Gaussian for a large class of partitions. For more quantitative results, see [9]. General combinatorial inequalities for p (n; m) are developed in [11] which are especially useful for partitions with a small number of summands. Appendix. In this appendix, we sketch the proof of (11) details can be found in [9] In Meinardus s original paper, the error term for p (n) in ....
[Article contains additional citation context not shown here]
H.-K. Hwang, Limit theorems for the number of summands in integer partitions, submitted.
Measures of Distinctness for Random Partitions and Compositions .. - Hwang, Yeh (1997) (4 citations) Self-citation (Hwang) (Correct)
....particular, he rederived the result of Erdos and Lehner for the mean number of distinct summands in a random partition. Central limit theorems for the number of 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, 32] They derived some combinatorial properties of the number and sum of distinct parts using an elementary approach. Another paper by Richmond and Knopfmacher ....
.... P (ff) if ff Gamma1; log log n; if ff = Gamma1; 2 Gamma(ff 1) 3n) ff 1) 2 (ff Gamma1) 2 ; if ff Gamma1: 4. 3 Partitions with small number of distinct summands Central and local limit theorems for the number of distinct parts in a random partition have been studied in Hwang [26] under a scheme essentially due to Meinardus [38] see also [21, 45] We consider in this section the distribution of integer partitions with small number of distinct parts. Our arguments rely on some new combinatorial inequalities which are interesting per se. Define two quantities by the ....
[Article contains additional citation context not shown here]
H.-K. Hwang. Limit theorems for the number of summands in integer partitions. submitted.
Measures of Distinctness for Random Partitions and Compositions .. - Hwang, Yeh (1997) (4 citations) Self-citation (Hwang) (Correct)
....particular, he rederived the result of Erdos and Lehner for the mean number of distinct summands in a random partition. Central limit theorems for the number of 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, 32] They derived some combinatorial properties of the number and sum of distinct parts using an elementary approach. Another paper by Richmond and Knopfmacher ....
....(#s 1) Corollary 8 If # is the set of prime numbers, then # # # P (#) if # 2#(# 1) 3n) # 1) 2 1. 4. 3 Partitions with small number of distinct summands Central and local limit theorems for the number of distinct parts in a random # partition have been studied in Hwang [26] under a scheme essentially due to Meinardus [38] see also [21, 45] We consider in this section the distribution of integer partitions with small number of distinct parts. Our arguments rely on some new combinatorial inequalities which are interesting per se. Define two quantities by the ....
[Article contains additional citation context not shown here]
H.-K. Hwang. Limit theorems for the number of summands in integer partitions. submitted.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC