An overpartition analogue of the q-binomial coefficients

作者：Dousse Jehanne; Kim Byungchan^*

来源：Ramanujan Journal, 2017, 42(2): 267-283.

DOI：10.1007/s11139-015-9718-4

• q-Binomial coefficients
• Gaussian Polynomial
• Overpartitions
• Rogers-Ramanujan type identity

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.

• 出版日期2017-2