On some infinite families of congruences for [j, k]-partitions into even parts distinct

M. S. Mahadeva Naika (), T. Harishkumar () and T. N. Veeranayaka ()
Additional contact information
M. S. Mahadeva Naika: Bengaluru City University
T. Harishkumar: Bangalore University
T. N. Veeranayaka: Bangalore University

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 4, 1038-1054

Abstract: Abstract In this paper, we define the partition function $$ped_{j, k}(n),$$ p e d j , k ( n ) , the number of [j, k]-partitions of n into even parts distinct, where none of the parts are congruent to $$j \;{\text{(mod k)}}$$ j (mod k) (where $$k >j\ge 1)$$ k > j ≥ 1 ) . We obtain many infinite families of congruences modulo powers of 2 for $$ped_{3, 6}(n)$$ p e d 3 , 6 ( n ) and congruences modulo powers of 2 and 3 for $$ped_{9, 18}(n)$$ p e d 9 , 18 ( n ) . For example, for all $$n \ge 0$$ n ≥ 0 and $$\alpha , \beta \ge 0,$$ α , β ≥ 0 , $$\begin{aligned} ped_{9, 18}\left(2\cdot 3^{4\alpha +4}\cdot 7^{2\beta +1} (7n+s)+\dfrac{11\cdot 3^{4\alpha +3}\cdot 7^{2\beta +1}+1}{4}\right)\equiv 0 \;{\text{(mod 16)}}, \end{aligned}$$ p e d 9 , 18 2 · 3 4 α + 4 · 7 2 β + 1 ( 7 n + s ) + 11 · 3 4 α + 3 · 7 2 β + 1 + 1 4 ≡ 0 (mod 16) , where $$s = 0, 2, 3, 4, 5, 6.$$ s = 0 , 2 , 3 , 4 , 5 , 6 .

Keywords: Congruences; Partitions with even parts distinct; [j k]-partitions; 05A17; 11P83 (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-021-00046-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:52:y:2021:i:4:d:10.1007_s13226-021-00046-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-021-00046-3

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().