More infinite families of congruences modulo 5 for broken 2-diamond partitions

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• 作者：Ernest X.W. Xia ^{ernestxwxia@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11P83 ; 05A17
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：170
• 期：Complete
• 页码：250-262
• 全文大小：291 K

文摘

The notion of broken k  -diamond partitions was introduced by Andrews and Paule. Let id="mmlsi1" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301020&_mathId=si1.gif&_user=111111111&_pii=S0022314X16301020&_rdoc=1&_issn=0022314X&md5=74095ec4d0b370bb513ecfed5bed3613" title="Click to view the MathML source">Δ_k(n)lass="mathContainer hidden">lass="mathCode">img="si1.gif" overflow="scroll">i mathvariant="normal">Δi>i>ki>lse">(i>ni>lse">) denote the number of broken k-diamond partitions of n for a fixed positive integer k  . Recently, Chan, and Paule and Radu proved some congruences modulo 5 for id="mmlsi2" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301020&_mathId=si2.gif&_user=111111111&_pii=S0022314X16301020&_rdoc=1&_issn=0022314X&md5=859922fa513808ab26728e0ddd116abb" title="Click to view the MathML source">Δ₂(n)lass="mathContainer hidden">lass="mathCode">img="si2.gif" overflow="scroll">i mathvariant="normal">Δi>2lse">(i>ni>lse">). In this paper, we prove several new infinite families of congruences modulo 5 for id="mmlsi2" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301020&_mathId=si2.gif&_user=111111111&_pii=S0022314X16301020&_rdoc=1&_issn=0022314X&md5=859922fa513808ab26728e0ddd116abb" title="Click to view the MathML source">Δ₂(n)lass="mathContainer hidden">lass="mathCode">img="si2.gif" overflow="scroll">i mathvariant="normal">Δi>2lse">(i>ni>lse">) by using an identity due to Newman. Our results generalize the congruences proved by Paule and Radu.