2018
DOI: 10.1142/s1793042118500641
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Congruences for some partitions related to mock theta functions

Abstract: Partitions related to mock theta functions were widely studied in the literature. Recently, Andrews et al. introduced two new kinds of partitions counted by [Formula: see text] and [Formula: see text], whose generating functions are [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text] are two third mock theta functions. Meanwhile, they obtained some congruences for [Formula: see text], [Formula: see text], and the associated smallest parts function [Formula: see text].… Show more

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Cited by 5 publications
(5 citation statements)
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“…There are several congruences for spt ω (n) modulo 11 and powers of 2 and 3 (For example, see [6,28,14]). But for modulo 5, to our knowledge, the following congruence, found by Andrews et al [6], is the only available one: spt ω (10n + 6) ≡ 0 (mod 5).…”
Section: And (132)mentioning
confidence: 99%
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“…There are several congruences for spt ω (n) modulo 11 and powers of 2 and 3 (For example, see [6,28,14]). But for modulo 5, to our knowledge, the following congruence, found by Andrews et al [6], is the only available one: spt ω (10n + 6) ≡ 0 (mod 5).…”
Section: And (132)mentioning
confidence: 99%
“…They also proved several congruences modulo 2 and infinite families of congruences modulo 4 and modulo 8 for p ω (n) and p ν (n). Motivated by the works in [5,7], Wang [28] and Cui, Gu and Hao [14] found many new congruences satisfied by p ω (n) and p ν (n) modulo 11 and modulo powers of 2 and 3. In particular, Wang [28] derived the following exact generating functions: .…”
Section: Introductionmentioning
confidence: 99%
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“…Moreover, they [2] derived several congruences modulo 2, 3, 4, 5 and 6 for spt ω (n). Soon after, Wang [15] as well as Cui, Gu and Hao [10] also established several new congruences modulo powers of 2 and 3 satisfied by spt ω (n). In particular, Wang [15] proved the following generating function:…”
Section: Introductionmentioning
confidence: 98%
“…product or quotient of certain q-shifted factorials). The interested readers may refer to [2,6,13] for details. Since the r.h.s.…”
Section: Introductionmentioning
confidence: 99%