Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897195 | Journal of Number Theory | 2017 | 17 Pages |
Abstract
Recently, Andrews defined combinatorial objects which he called singular overpartitions and proved that these singular overpartitions which depend on two parameters k and i can be enumerated by the function Câ¾k,i(n), which denotes the number of overpartitions of n in which no part is divisible by k and only parts â¡Â±i(modk) may be overlined. G.E. Andrews, S.C. Chen, M. Hirschhorn, J.A. Sellars, Olivia X.M. Yao, M.S. Mahadeva Naika, D.S. Gireesh, Zakir Ahmed and N.D. Baruah noted numerous congruences modulo 2,3,4,6,12,16,18,32 and 64 for Câ¾3,1(n). In this paper, we prove congruences modulo 128 for Câ¾3,1(n), and congruences modulo 2 for Câ¾12,3(n), Câ¾44,11(n),Câ¾75,15(n), and Câ¾92,23(n). We also prove “Mahadeva Naika and Gireesh's conjecture”, for nâ¥0, Câ¾3,1(12n+11)â¡0(mod144) is true.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
T. Kathiravan, S.N. Fathima,