On a 3-Way Combinatorial Identity

• 作者: Ashok Kumar Agarwal Garima Sood
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: Basic Series PARTITIONS N-Colour PARTITIONS FROBENIUS PARTITIONS LATTICE PATHS GENERATING Functions Combinatorial IDENTITIES
• 年，卷（期）: 2014,（4）
• 页码范围: 89-96
• 页数: 8页
• 分类号: O1

摘要

Recently in [1] Goyal and Agarwal interpreted a generalized basic series as a generating function for a colour partition function and a weighted lattice path function. This led to an infinite family of combinatorial identities. Using Frobenius partitions, we in this paper extend the result of [1] and obtain an infinite family of 3-way combinatorial identities. We illustrate by an example that our main result has a potential of yielding Rogers-Ramanujan-MacMahon type identities with convolution property.