An overpartition analogue of the q-binomial coefficients

被引:8
作者
Dousse, Jehanne [1 ]
Kim, Byungchan [2 ]
机构
[1] Univ Paris Diderot Paris 7, LIAFA, F-75205 Paris 13, France
[2] Seoul Natl Univ Sci & Technol, Sch Liberal Arts, 232 Gongreung Ro, Seoul 139743, South Korea
基金
新加坡国家研究基金会;
关键词
q-Binomial coefficients; Gaussian Polynomial; Overpartitions; Rogers-Ramanujan type identity; CONGRUENCES; THEOREM; RANK;
D O I
10.1007/s11139-015-9718-4
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We define an overpartition analogue of Gaussian polynomials (also known as q-binomial coefficients) as a generating function for the number of overpartitions fitting inside the rectangle. We call these new polynomials over Gaussian polynomials or over q-binomial coefficients. We investigate basic properties and applications of over q-binomial coefficients. In particular, via the recurrences and combinatorial interpretations of over q-binomial coefficients, we prove a Rogers-Ramanujan type partition theorem.
引用
收藏
页码:267 / 283
页数:17
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