Combinatorics of two second-order mock theta functions

被引：2
|
作者：
Burson, Hannah [1 ]
机构：
[1] Univ Minnesota, Sch Math, Vincent Hall,206 Church St SE, Minneapolis, MN 55455 USA
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2021年 / 17卷 / 02期
关键词：
Partitions; mock theta functions; q-series;
D O I：
10.1142/S1793042120400229
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce combinatorial interpretations of the coefficients of two second-order mock theta functions. Then, we provide a bijection that relates the two combinatorial interpretations for each function. By studying other special cases of the multivariate identity proved by the bijection, we obtain new combinatorial interpretations for the coefficients of Watson's third-order mock theta function omega(q) and Ramanujan's third-order mock theta function f(q).
引用
收藏
页码：285 / 295
页数：11
相关论文
共 50 条
  • [21] Families of multisums as mock theta functions
    Gu, Nancy S. S.
    Liu, Jing
    ADVANCES IN APPLIED MATHEMATICS, 2016, 79 : 98 - 124
  • [22] Parity of coefficients of mock theta functions
    Wang, Liuquan
    JOURNAL OF NUMBER THEORY, 2021, 229 : 53 - 99
  • [23] Asymptotic Behaviour of Another Second Order Mock Theta Function
    Srivastava, Bhaskar
    KYUNGPOOK MATHEMATICAL JOURNAL, 2007, 47 (03): : 341 - 345
  • [24] Combinatorial interpretations as two-line array for the mock theta functions
    Eduardo H. M. Brietzke
    José Plínio O. Santos
    Robson da Silva
    Bulletin of the Brazilian Mathematical Society, New Series, 2013, 44 : 233 - 253
  • [25] A Note on Certain Properties of Mock Theta Functions of Order Eight
    Srivastava, Pankaj
    Wahidi, Anwar Jahan
    KYUNGPOOK MATHEMATICAL JOURNAL, 2014, 54 (02): : 249 - 262
  • [26] IDENTITIES INVOLVING MOCK THETA FUNCTIONS AND THETA FUNCTIONS
    Song, Hanfei
    Wang, Chun
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 151 (07) : 3009 - 3022
  • [27] Generalizations of mock theta functions
    Cui, Su-Ping
    Gu, Nancy S. S.
    Su, Chen-Yang
    Xie, Matthew H. Y.
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2024, 20 (09) : 2395 - 2413
  • [28] Modular Tranformations for Ramanujan's Tenth Order Mock Theta Functions
    Srivastava, Bhaskar
    KYUNGPOOK MATHEMATICAL JOURNAL, 2005, 45 (02): : 211 - 220
  • [29] On two 10th-order mock theta identities
    Jeremy Lovejoy
    Robert Osburn
    The Ramanujan Journal, 2015, 36 : 117 - 121
  • [30] On two 10th-order mock theta identities
    Lovejoy, Jeremy
    Osburn, Robert
    RAMANUJAN JOURNAL, 2015, 36 (1-2) : 117 - 121
12345