New generalization of cubic partition of ![n](http://212.189.136.205/plugins/generic/latexRender/cache/7b8b965ad4bca0e41ab51de7b31363a1.png)
Abstract
Let
be the generalization of the cubic partition function
. In this paper, we prove some new congruences modulo odd prime
by taking
and
using
-series identities. We study congruence properties of generalization of cubic partition function for different values of
and give some particular cases as examples.
![c^*_{(1,r,a)}(n)](http://212.189.136.205/plugins/generic/latexRender/cache/5fcbf0358fc9a877240b562b75c263ee.png)
![c(n)](http://212.189.136.205/plugins/generic/latexRender/cache/6f92aad59cd2c0646a2f0c5844875990.png)
![p](http://212.189.136.205/plugins/generic/latexRender/cache/83878c91171338902e0fe0fb97a8c47a.png)
![r=3,4,5,7,11](http://212.189.136.205/plugins/generic/latexRender/cache/5be1bec8a0117869192867f8ef6af3ad.png)
![13](http://212.189.136.205/plugins/generic/latexRender/cache/c51ce410c124a10e0db5e4b97fc2af39.png)
![q](http://212.189.136.205/plugins/generic/latexRender/cache/7694f4a66316e53c8cdd9d9954bd611d.png)
![a](http://212.189.136.205/plugins/generic/latexRender/cache/0cc175b9c0f1b6a831c399e269772661.png)
DOI Code:
10.1285/i15900932v42n2p7
Keywords:
Partitions; k-colors; Partition Congruences
Full Text: PDF