Multi-partition analogue of q-binomial coefficients

IF 0.5 3区数学 Q3 MATHEMATICS International Journal of Number Theory Pub Date : 2024-03-20 DOI:10.1142/s1793042124500659

Byungchan Kim, Hayan Nam, Myungjun Yu

引用次数: 0

Abstract

We introduce the multi-Gaussian polynomial $G_{k} (M, N)$ , a multi-partition analogue of the Gaussian polynomial (also known as $q$ -binomial coefficient), as the generating function for certain restricted multi-color partitions. We study basic properties of multi-Gaussian polynomials and non-symmetric properties of $G_{k} (M, N)$ . We also derive a Sylvester-type identity and its application.

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q 次二项式系数的多分区类似物

我们介绍了多高斯多项式 Gk(M,N)，它是高斯多项式（又称 q-二项式系数）的多分区类似物，是某些受限多色分区的生成函数。我们研究了多高斯多项式的基本性质和 Gk(M,N) 的非对称性质。我们还推导出了一个西尔维斯特式特性及其应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.

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