scholarly journals Partition Theoretic Interpretation of Two Identities of Euler

2020 ◽  
Vol 19 ◽  
pp. 96-98
Author(s):  
Ananta Kr Bora
Keyword(s):  
Partition Function ◽  
Generating Function ◽  
Restricted Partition

In this paper, we have derived a generating function for a restricted partition function. This is in conjunction with two identities of Euler provides a new partition theoretic interpretation of two identities of Euler.

scholarly journals New Partition Theoretic Interpretations of Rogers-Ramanujan Identities

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
A. K. Agarwal ◽  
M. Goyal
Keyword(s):  
Partition Function ◽  
Generating Function ◽  
Restricted Partition

The generating function for a restricted partition function is derived. This in conjunction with two identities of Rogers provides new partition theoretic interpretations of Rogers-Ramanujan identities.

scholarly journals Untrodden pathways in the theory of the restricted partition function p(n,N)

2021 ◽  
Vol 180 ◽  
pp. 105423
Author(s):  
Atul Dixit ◽  
Pramod Eyyunni ◽  
Bibekananda Maji ◽  
Garima Sood
Keyword(s):  
Partition Function ◽  
Restricted Partition

scholarly journals On the restricted partition function

2018 ◽  
Vol 47 (3) ◽  
pp. 565-588 ◽  
Author(s):  
Mircea Cimpoeaş ◽  
Florin Nicolae
Keyword(s):  
Partition Function ◽  
Restricted Partition

Ramanujan Congruences For p-k(n) Modulo Powers Of 17

1991 ◽  
Vol 43 (3) ◽  
pp. 506-525 ◽  
Author(s):  
Kim Hughes
Keyword(s):  
Partition Function ◽  
Generating Function ◽  
Ramanujan Congruences ◽  
Image Position

For each integer r we define the sequence pr(n) by We note that p-1(n) = p(n), the ordinary partition function. On account of this some authors set r = — k to make positive values of k correspond to positive powers of the generating function for p(n): We follow this convention here. In [3], Atkin proved the following theorem.

Inverse Problems for Partition Functions

2001 ◽  
Vol 53 (4) ◽  
pp. 866-896
Author(s):  
Yifan Yang
Keyword(s):  
Asymptotic Behavior ◽  
Partition Function ◽  
Inverse Problems ◽  
Large Class ◽  
Generating Function ◽  
Riemann Hypothesis ◽  
Arithmetic Function ◽  
Partition Functions ◽  
Class Of Functions ◽  
Weighted Partition

AbstractLet pw(n) be the weighted partition function defined by the generating function , where w(m) is a non-negative arithmetic function. Let be the summatory functions for pw(n) and w(n), respectively. Generalizing results of G. A. Freiman and E. E. Kohlbecker, we show that, for a large class of functions Φ(u) and λ(u), an estimate for Pw(u) of the formlog Pw(u) = Φ(u){1 + Ou(1/λ(u))} (u→∞) implies an estimate forNw(u) of the formNw(u) = Φ*(u){1+O(1/ log ƛ(u))} (u→∞) with a suitable function Φ*(u) defined in terms of Φ(u). We apply this result and related results to obtain characterizations of the Riemann Hypothesis and the Generalized Riemann Hypothesis in terms of the asymptotic behavior of certain weighted partition functions.

Corrigendum to “on the restricted partition function”

2019 ◽  
Vol 49 (3) ◽  
pp. 699-700
Author(s):  
Mircea Cimpoeaş ◽  
Florin Nicolae
Keyword(s):  
Partition Function ◽  
Restricted Partition

scholarly journals Brane webs and random processes

2015 ◽  
Vol 30 (33) ◽  
pp. 1550202 ◽  
Author(s):  
Amer Iqbal ◽  
Babar A. Qureshi ◽  
Khurram Shabbir ◽  
Muhammad A. Shehper
Keyword(s):  
Partition Function ◽  
Boundary Conditions ◽  
Generating Function ◽  
Random Processes ◽  
Open String ◽  
Plane Partitions ◽  
Schur Process ◽  
String Amplitudes

We study (p, q) 5-brane webs dual to certain N M5-brane configurations and show that the partition function of these brane webs gives rise to cylindric Schur process with period N. This generalizes the previously studied case of period 1. We also show that open string amplitudes corresponding to these brane webs are captured by the generating function of cylindric plane partitions with profile determined by the boundary conditions imposed on the open string amplitudes.

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