The ranks and cranks of partitions moduli 2, 3, and 4

被引:46
作者
Andrews, GA
Lewis, R
机构
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
[2] Univ Sussex, Sch Math Sci, Brighton BN1 9QH, E Sussex, England
关键词
D O I
10.1006/jnth.2000.2537
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We discuss inequalities between the rank counts N(r,m,n) and between the crank counts M(r,m,n). for m = 2, 3, and 4. and state three conjectures. (C) 2000 Academic Press.
引用
收藏
页码:74 / 84
页数:11
相关论文
共 11 条
[1]   On a conjecture of Peter Borwein [J].
Andrews, GE .
JOURNAL OF SYMBOLIC COMPUTATION, 1995, 20 (5-6) :487-501
[2]   RAMANUJAN LOST NOTEBOOK .7. THE 6TH ORDER MOCK THETA FUNCTIONS [J].
ANDREWS, GE ;
HICKERSON, D .
ADVANCES IN MATHEMATICS, 1991, 89 (01) :60-105
[3]  
Atkin A.O.L., 1954, Proc. Lond. Math. Soc., V4, P84, DOI DOI 10.1112/PLMS/S3-4.1.84
[4]  
Dyson F.J., 1944, Eureka, V8, P10
[5]  
Ekin AB, 1998, J COMB THEORY A, V83, P283
[6]  
Garvan F.G., 1988, RAMANUJAN REVISITED, P29
[7]  
Garvan F.G., 1986, THESIS PENNSYLVANIA
[8]   NEW COMBINATORIAL INTERPRETATIONS OF RAMANUJAN PARTITION CONGRUENCES MOD-5, MOD-7 AND MOD-11 [J].
GARVAN, FG .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 305 (01) :47-77
[9]   The ranks of partitions modulo 2 [J].
Lewis, RP .
DISCRETE MATHEMATICS, 1997, 167 :445-449
[10]  
Watson G.N., 1936, J LOND MATH SOC, V11, P55, DOI DOI 10.1112/JLMS/S1-11.1.55