关于卷积型组合恒等式的格路方法(Ⅱ)——赋权格路的枚举函数方法

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On the Lattice Path Method in Convolution Type Combinatorial ldentities(Ⅱ)——The Weighted Counting Function Method on Lattice Paths

摘要: 作为无限制条件下格路计数函数——Gauss多项式系数的自然拓广,作者研究了赋权格路的枚举问题.对应的卷积计算则产生普通多项式系数和Gauss的q-多项式系数的Vandermonde组合恒等式.

Abstract: An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identities for multinomial and q-multinomial coefficients.

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