Congruences modulo 7 for broken 3-diamond partitions

被引：0
作者：
Eric H. Liu
Wenjing Du
机构：
[1] Shanghai University of International Business and Economics,School of Statistics and Information
[2] East China University of Political Science and Law,Wenbo College
来源：
The Ramanujan Journal | 2019年 / 50卷
关键词：
Broken ; -diamond partition; Congruence; Theta function; 11P83; 05A17;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In 2007, Andrews and Paule introduced the notion of broken k-diamond partitions. Let Δk(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta _k(n)$$\end{document} denote the number of broken k-diamond partitions of n for a fixed positive integer k. Recently, Wang and Yao, and Xia proved several infinite families of congruences modulo 7 for Δ3(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta _3(n)$$\end{document} by using theta function identities. In this paper, we give a new proof of one result of Wang and Yao, and find three new infinite families of congruences modulo 7 for Δ3(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta _3(n)$$\end{document}.
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页码：253 / 262
页数：9
相关论文
共 11 条
[1]  
Andrews GE(2007)MacMahon’s partition analysis XI: broken diamonds and modular forms Acta Arithm. 126 281-294
[2]  
Paule P(2013)Congruences for broken Ann. Combin. 17 333-338
[3]  
Jameson M(2010)-diamond partitions Ramanujan J. 23 409-416
[4]  
Paule P(2016)Infinite families of strange partition congruences for broken 2-diamonds Ramanujan J. 40 389-403
[5]  
Radu S(2017)Infinite families of congruences modulo 7 for broken 3-diamond partitions J. Number Theory 170 250-262
[6]  
Xia EXW(2017)More infinite families of congruences modulo 5 for broken 2-diamond partitions Ramanujan J. 42 301-323
[7]  
Xia EXW(2011)Congruences modulo 9 and 27 for overpartitions Proc. Jpn. Acad. Ser. A (Math. Sci.) 87 65-68
[8]  
Xia EXW(2017)Two congruences involving Andrews–Paule’s broken Ramanujan J. 43 619-631
[9]  
Xiong X(undefined)-diamond partitions and 5-diamond partitions undefined undefined undefined-undefined
[10]  
Yao OXM(undefined)Newman’s identity and infinite families of congruences modulo 7 for broken 3-diamond partitions undefined undefined undefined-undefined
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