Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Kathy Q. Ji"'
Publikováno v:
The Ramanujan Journal.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8fffaf9369ace5566661c9be19d224be
https://doi.org/10.1007/s11139-022-00687-w
https://doi.org/10.1007/s11139-022-00687-w
Publikováno v:
Journal of Combinatorial Theory, Series A. 166:254-296
In 1967, Andrews found a combinatorial generalization of the Gollnitz-Gordon theorem, which can be called the Andrews-Gollnitz-Gordon theorem. In 1980, Bressoud derived a multisum Rogers-Ramanujan-type identity, which can be considered as the generat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dde0d501c7d54f85c3bfa5b9131be4a0
https://doi.org/10.1016/j.jcta.2019.02.021
https://doi.org/10.1016/j.jcta.2019.02.021
Publikováno v:
Journal of Number Theory. 184:235-269
Lovejoy and Osburn proved formulas for the generating functions for the rank differences of overpartitions modulo 3 and 5. In this paper, we derive formulas for the generating functions for the rank differences of overpartitions modulo 6 and 10. With
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0d7d16280de02b72d53a3669c1915f6c
https://doi.org/10.1016/j.jnt.2017.08.021
https://doi.org/10.1016/j.jnt.2017.08.021
Autor:
Alice X.H. Zhao, Kathy Q. Ji
Publikováno v:
The Ramanujan Journal. 44:631-640
In this note, we introduce the 2kth crank moment \(\mu _{2k}(-1,n)\) weighted by the parity of cranks and show that \((-1)^n \mu _{2k}(-1,n)>0\) for \(n\ge k \ge 0\). When \(k=0\), the inequality \((-1)^n \mu _{2k}(-1,n)>0\) reduces to Andrews and Le
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8e3d063290c3d820b7257d4979b4bcee
https://doi.org/10.1007/s11139-016-9828-7
https://doi.org/10.1007/s11139-016-9828-7
Publikováno v:
International Journal of Number Theory. 12:1475-1482
By constructing a sign-reversing involution, we prove Warnaar’s identity involving a partial theta function, which plays many important roles in the study of asymptotic behaviors and quantum modularities in number theory. We also obtain an Euler-li
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::264a67e68704a8f2b5bdba31c4b4a02d
https://doi.org/10.1142/s1793042116500901
https://doi.org/10.1142/s1793042116500901
Publikováno v:
European Journal of Combinatorics. 51:255-267
Recently, Andrews and Merca considered the truncated version of Euler's pentagonal number theorem and obtained a non-negative result on the coefficients of this truncated series. Guo and Zeng showed the coefficients of two truncated Gauss' identities
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d5a5b4944007db4b77ed222cce2495f0
https://doi.org/10.1016/j.ejc.2015.05.014
https://doi.org/10.1016/j.ejc.2015.05.014
Autor:
Wenston J.T. Zang, Kathy Q. Ji
The main objective of this paper is to investigate the distribution of the Andrews-Garvan-Dyson crank of a partition. Let $M(m,n)$ denote the number of partitions of $n$ with the Andrews-Garvan-Dyson crank $m$, we show that the sequence \break $\{M(m
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::38e9c5250ef76342f0d8b67952187fbc
http://arxiv.org/abs/1811.07321
http://arxiv.org/abs/1811.07321
Autor:
Alice X.H. Zhao, Kathy Q. Ji
Publikováno v:
Advances in Applied Mathematics. 65:65-86
Recently, Garvan obtained two-variable Hecke-Rogers identities for three universal mock theta functions g 2 ( z ; q ) , g 3 ( z ; q ) , K ( z ; q ) by using basic hypergeometric functions, and he proposed a problem of finding direct proofs of these i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8ba49a10df6d46dc4cf76b0eec47c32b
https://doi.org/10.1016/j.aam.2015.02.001
https://doi.org/10.1016/j.aam.2015.02.001
Publikováno v:
Advances in Mathematics. 270:60-96
The spt-crank of a vector partition, or an S-partition, was introduced by Andrews, Garvan and Liang. Let N S ( m , n ) denote the net number of S-partitions of n with spt-crank m, that is, the number of S-partitions ( π 1 , π 2 , π 3 ) of n with s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a64cf057f6fc92e8ee39978008756f08
https://doi.org/10.1016/j.aim.2014.10.017
https://doi.org/10.1016/j.aim.2014.10.017
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9783319683751
Let \(N(\le m,n)\) denote the number of partitions of n with rank not greater than m, and let \(M(\le m,n)\) denote the number of partitions of n with crank not greater than m. Bringmann and Mahlburg observed that \(N(\le m,n)\le M(\le m,n)\le N(\le
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::433c775184e02bfeb3b6653b91b73503
https://doi.org/10.1007/978-3-319-68376-8_11
https://doi.org/10.1007/978-3-319-68376-8_11