Generalized congruence properties of the restricted partition function p(n,m)

2012 ◽  
Vol 30 (3) ◽  
pp. 425-436 ◽  
Author(s):  
Brandt Kronholm
Keyword(s):  
Partition Function ◽  
Restricted Partition ◽  
Congruence Properties

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 On congruence properties of the partition function

2000 ◽  
Vol 23 (7) ◽  
pp. 493-496 ◽  
Author(s):  
Jayce Getz
Keyword(s):  
Partition Function ◽  
Congruence Properties

Some congruence properties of the partition function are proved.

On congruence properties of the restricted partition functions $$p_{\omega }(n,k)$$ p ω ( n , k ) and $$p_{\nu }(n,k)$$ p ν ( n , k )

2018 ◽  
Vol 49 (1) ◽  
pp. 105-113
Author(s):  
Robson da Silva ◽  
Kelvin Souza de Oliveira ◽  
Almir Cunha da Graça Neto
Keyword(s):  
Partition Functions ◽  
Restricted Partition ◽  
Congruence Properties

Ramanujan Congruences for p-k(n)

1968 ◽  
Vol 20 ◽  
pp. 67-78 ◽  
Author(s):  
A. O. L. Atkin
Keyword(s):  
Partition Function ◽  
Ramanujan Congruences ◽  
Image Position ◽  
Congruence Properties

Let12Thus p-1(n) = p(n) is just the partition function, for which Ramanujan (4) found congruence properties modulo powers of 5, 7, and 11. Ramanathan (3) considers the generalization of these congruences modulo powers of 5 and 7 for all ; unfortunately his results are incorrect, because of an error in his Lemma 4 on which his main theorems depend. This error is essentially a misquotation of the results of Watson (5), which one may readily understand in view of Watson's formidable notation.

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.

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