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Some new congruences for simultaneously $s$-regular and $t$-distinct partition function
P. Buragohain,
N. Saikia Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh, 791112 India
Abstract:
A partition of a positive integer
$n$ is said to be simultaneously
$s$-regular and
$t$-distinct partition if none of the parts is divisible by
$s$ and parts appear fewer than
$t$ times. In this paper, we present some new congruences for simultaneously
$s$-regular and
$t$-distinct partition function denoted by
$ M_{s,t}^d (n)$ with $(s,t) \in \{(2,5),(3,4), (4,9), (5\alpha,5\beta),(7\alpha,7\beta),(p,p)\}$, where
$\alpha$ and
$\beta$ are any positive integers and
$p$ is any prime.
Keywords:
$s$-regular and $t$-distinct partition, congruence, $q$-series identities.
UDC:
517 Received: 07.12.2023
Revised: 30.12.2023
Accepted: 20.03.2024
DOI:
10.26907/0021-3446-2024-10-18-21
Fulltext:
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