An overpartition analogue of the q-binomial coefficients

2014/10/20 by Jehanne Dousse, Dousse, Jehanne, Byungchan Kim +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1410.5301

v2: new section added about another way of proving our theorems using q-series identities

openalex publication_date 2014/10/20 · arxiv created 2014/12/27 · arxiv updated 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 M × N 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-Ramaujan type partition theorem.

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