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New congruences for 4,6-regular partitions modulo primes · arXivDesk

2308.04752Aug 9, 202313 pages. v2: Append results for b_4(n) modulo 2, b_6(n) modulo 5. v3: We find two explicit infinite families of b_4(n) modulo 3. See Theorem 1.2

New congruences for 4,6-regular partitions modulo primes

Qi-Yang Zheng

Abstract

The main result of the paper is the existence of an infinitely many families of Ramanujan-type congruences for $b_4(n)$ and $b_6(n)$ modulo primes $m \geq 2$

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and

m \geq 5

, respectively. We provide new examples of congruences for

b_4(n)

and

b_6(n)

. Moreover, we find two infinite explicit infinite families of congruences for

b_4(n)

modulo

3

.

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