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Let
Abstract
Purpose
Let
Design/methodology/approach
H.C. Chan has studied the congruence properties of cubic partition function a(n), which is defined by
Findings
To establish several congruence modulo 8 for
Originality/value
The results established in the work are extension to those proved in ℓ-regular cubic partition pairs.
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Keywords
Abstract
Purpose
Let p[1,r;t] be defined by
Design/methodology/approach
Using q-series expansion/identities, the authors established general congruence modulo prime number for two-colour partition function.
Findings
In the paper, the authors study congruence properties of two-colour partition function for fractional values. The authors also give some particular cases as examples.
Originality/value
The partition functions for fractional value is studied in 2019 by Chan and Wang for Ramanujan's general partition function and then extended by Xia and Zhu in 2020. In 2021, Baruah and Das also proved some congruences related to fractional partition functions previously investigated by Chan and Wang. In this sequel, some congruences are proved for two-colour partitions in this paper. The results presented in the paper are original.
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Keywords
S. Shivaprasada Nayaka, T.K. Sreelakshmi and Santosh Kumar
In this paper, the author defines the function
Abstract
Purpose
In this paper, the author defines the function
Design/methodology/approach
Andrews introduced to combinatorial objects, which he called singular overpartitions and proved that these singular overpartitions depend on two parameters δ and i can be enumerated by the function
Findings
Using classical spirit of q-series techniques, the author obtains congruences modulo 4 for
Originality/value
The results established in this work are extension to those proved in Andrews’ singular overpatition pairs of n.
Details