Arithmetic Properties of 9-Regular Partitions with Distinct Odd Parts

Let pod 9 ( n ) , ped 9 ( n ) , and A ¯ 9 ( n ) denote the number of 9-regular partitions of n wherein odd parts are distinct, even parts are distinct, and the number of 9-regular overpartitions of n , respectively. By considering pod 9 ( n ) from an arithmetic point of view, we establish a number o...

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Bibliographic Details
Published in:Acta mathematica vietnamica 2019-09, Vol.44 (3), p.797-811
Main Authors: Hemanthkumar, B., Bharadwaj, H. S. Sumanth, Naika, M. S. Mahadeva
Format: Article
Language:English
Subjects:
Arithmetic
Congruences
Mathematics
Mathematics and Statistics
Partitions (mathematics)
Progressions
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Summary:Let pod 9 ( n ) , ped 9 ( n ) , and A ¯ 9 ( n ) denote the number of 9-regular partitions of n wherein odd parts are distinct, even parts are distinct, and the number of 9-regular overpartitions of n , respectively. By considering pod 9 ( n ) from an arithmetic point of view, we establish a number of infinite families of congruences modulo 16 and 32, and some internal congruences modulo small powers of 3. A relation connecting above partition functions in arithmetic progressions is obtained as follows. For any n ≥ 0 , 6 pod 9 ( 2 n + 1 ) = 2 ped 9 ( 2 n + 3 ) = 3 A ¯ 9 ( n + 1 ) .
ISSN:0251-4184
2315-4144
DOI:10.1007/s40306-018-0274-z