Congruences for (3,11)-regular bipartitions modulo 11

被引：10

作者：

Dou, Donna Q. J. ^{[1
]}

机构：

[1] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China

来源：

RAMANUJAN JOURNAL | 2016年 / 40卷 / 03期

基金：

中国国家自然科学基金;

关键词：

(k; l)-Regular bipartition; Cubic theta functions; Congruence; REGULAR PARTITION-FUNCTIONS; EVEN PARTS DISTINCT; 9-REGULAR PARTITIONS; ARITHMETIC PROPERTIES; OVERPARTITION PAIRS; KEITHS CONJECTURE; DIVISIBILITY; IDENTITIES; RAMANUJAN; NUMBER;

D O I：

10.1007/s11139-015-9732-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note we investigate the function , which counts the number of -regular bipartitions of n. We shall prove an infinite family of congruences modulo 11: for alpha >= 2 and n >= 0, B-3,B-11 (3(alpha)n + 5.3(alpha-1) - 1/2) equivalent to 0 (mod 11).

引用

页码：535 / 540

页数：6

共 33 条

[1] The arithmetic of partitions into distinct parts [J].

Ahlgren, S ;

Lovejoy, J .

MATHEMATIKA, 2001, 48 (95-96) :203-211

[2] Arithmetic properties of partitions with even parts distinct [J].

Andrews, George E. ;

Hirschhorn, Michael D. ;

Sellers, James A. .

RAMANUJAN JOURNAL, 2010, 23 (1-3) :169-181

[3] SOME CUBIC MODULAR IDENTITIES OF RAMANUJAN [J].

BORWEIN, JM ;

BORWEIN, PB ;

GARVAN, FG .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 343 (01) :35-47

[4] Rank and congruences for overpartition pairs [J].

Bringmann, Kathrin ;

Lovejoy, Jeremy .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2008, 4 (02) :303-322

[5] Infinite families of infinite families of congruences for k-regular partitions [J].

Carlson, Rowland ;

Webb, John J. .

RAMANUJAN JOURNAL, 2014, 33 (03) :329-337

[6] RAMANUJAN'S CUBIC CONTINUED FRACTION AND AN ANALOG OF HIS "MOST BEAUTIFUL IDENTITY" [J].

Chan, Hei-Chi .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2010, 6 (03) :673-680

[7] Pairs of partitions without repeated odd parts [J].

Chan, Song Heng ;

Mao, Renrong .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 394 (01) :408-415

[8] Arithmetic properties of overpartition pairs [J].

Chen, William Y. C. ;

Lin, Bernard L. S. .

ACTA ARITHMETICA, 2012, 151 (03) :263-277

[9] Congruences for bipartitions with odd parts distinct [J].

Chen, William Y. C. ;

Lin, Bernard L. S. .

RAMANUJAN JOURNAL, 2011, 25 (02) :277-293

[10] Congruences for 9-regular partitions modulo 3 [J].

Cui, Su-Ping ;

Gu, Nancy S. S. .

RAMANUJAN JOURNAL, 2015, 38 (03) :503-512

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