Asymptotic behavior of Odd-Even partitions

被引：0

作者：

Jang, Min-Joo ^{[1
]}

机构：

[1] Univ Cologne, Math Inst, D-50931 Cologne, Germany

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2017年 / 24卷 / 03期

基金：

欧洲研究理事会;

关键词：

Odd-Even partitions; Overpartitions; Asymptotics; Wright's circle method;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Andrews studied a function which appears in Ramanujan's identities. In Ramanujan's "Lost" Notebook, there are several formulas involving this function, but they are not as simple as the identities with other similar shape of functions. Nonetheless, Andrews found out that this function possesses combinatorial information, odd-even partition. In this paper, we provide the asymptotic formula for this combinatorial object. We also study its companion odd-even overpartitions.

引用

页数：15

共 15 条

[1] Andrews G., 1988, The Theory of Partitions
[2] Andrews G.E., 1986, NSF CBMS REGIONAL C, V66
[3] Andrews G.E., 2001, Special Functions, Encyclopedia of Mathematics and Its Applications
[4] RAMANUJAN LOST NOTEBOOK .4. STACKS AND ALTERNATING PARITY IN PARTITIONS
ANDREWS, GE
[J]. ADVANCES IN MATHEMATICS, 1984, 53 (01) : 55 - 74
[5] [Anonymous], 1941, ANN MATH
[6] Bringmann K., 2015, ELECTRON J COMB, V22
[7] Hardy GH, 1918, P LOND MATH SOC, V17, P75
[8] KOBLITZ N., 1984, Graduate Texts in Mathematics, V97
[9] Rank and conjugation for a second Frobenius representation of an overpartition
Lovejoy, Jeremy
[J]. ANNALS OF COMBINATORICS, 2008, 12 (01) : 101 - 113
[10] SOME ASYMPTOTIC FORMULAS FOR Q-HYPERGEOMETRIC SERIES
MCINTOSH, RJ
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1995, 51 : 120 - 136

← 1 2 →