scholarly journals On the Restricted Partition Function via Determinants with Bernoulli Polynomials

2020 ◽  
Vol 17 (2) ◽  
Author(s):  
Mircea Cimpoeaş
Keyword(s):  
Partition Function ◽  
Bernoulli Polynomials ◽  
Restricted Partition

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

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 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 The Polynomial Part of a Restricted Partition Function Related to the Frobenius Problem

10.37236/1592 ◽  
2001 ◽  
Vol 8 (1) ◽  
Author(s):  
Matthias Beck ◽  
Ira M. Gessel ◽  
Takao Komatsu
Keyword(s):  
Partition Function ◽  
Explicit Formula ◽  
Nonnegative Integer ◽  
Frobenius Problem ◽  
Restricted Partition ◽  
Integer Solutions ◽  
Positive Integers

Given a set of positive integers $ A = \{ a_{1} , \dots , a_{n} \} $, we study the number $ p_{A} (t) $ of nonnegative integer solutions $ \left( m_{1} , \dots , m_{n} \right) $ to $ \sum_{j=1}^{n} m_{j} a_{j} = t $. We derive an explicit formula for the polynomial part of $p_A$.

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