An infinite family of congruences modulo $$3$$3 for $$13$$13-regular bipartitions
An infinite family of congruences modulo $$3$$3 for $$13$$13-regular bipartitions
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DOI：
10.1007/s11139-014-9610-7
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发表时间：
2016
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影响因子：
--
通讯作者：
Bernard L. S. Lin
中科院分区：
文献类型：
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作者：
Bernard L. S. Lin
Letdenote the number of-regular bipartitions of. Our goal is to consider this function from an arithmetical point of view in the spirit of Ramanujan’s congruences for the unrestricted partition function. In particular, we shall prove an infinite family of congruences: forand, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} B_{13}(3^{\alpha }n+2\cdot 3^{\alpha -1}-1)\equiv \ 0\ (\mathrm{mod\ }3). \end{aligned}$$\end{document}In addition, we will also give an alternative proof of one infinite family of congruences for, the number ofregular partitions of, due to Webb.
Letdenote the number of-regular bipartitions of. Our goal is to consider this function from an arithmetical point of view in the spirit of Ramanujan’s congruences for the unrestricted partition function. In particular, we shall prove an infinite family of congruences: forand, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} B_{13}(3^{\alpha }n+2\cdot 3^{\alpha -1}-1)\equiv \ 0\ (\mathrm{mod\ }3). \end{aligned}$$\end{document}In addition, we will also give an alternative proof of one infinite family of congruences for, the number ofregular partitions of, due to Webb.