Some new congruences for Andrews' singular overpartitions

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• 作者：T. Kathiravan¹ ; ^{kkathiravan98@gmail.com} ; S.N. Fathima ; ^{fathima.mat@pondiuni.edu.in}
• 关键词：11P83 ; 05A17
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：173
• 期：Complete
• 页码：378-393
• 全文大小：326 K
• 卷排序：173

文摘

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 C‾k,i(n), which denotes the number of overpartitions of n in which no part is divisible by k   and only parts ≡±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 2,3,4,6,12,16,18,322,3,4,6,12,16,18,32 and 64 for C‾3,1(n). In this paper, we prove congruences modulo 128 for C‾3,1(n), and congruences modulo 2 for C‾12,3(n), C‾44,11(n),C‾75,15(n), and C‾92,23(n). We also prove “Mahadeva Naika and Gireesh's conjecture”, for n≥0n≥0, C‾3,1(12n+11)≡0(mod144) is true.