Linear algebra and congruences for MacMahon’s k-rowed plane partitions

IF 0.5 3区数学 Q3 MATHEMATICS

International Journal of Number Theory Pub Date : 2024-03-20 DOI:10.1142/s1793042124500702

Shi-Chao Chen

引用次数: 0

Abstract

In this paper, we provide an algorithm to detect linear congruences of $p l_{k} (n)$ , the number of MacMahon’s $k$ -rowed plane partitions, and give a quantitative result on the nonexistence of Ramanujan-type congruences of the $k$ -rowed plane partition functions. We also show $p (n, m)$ that the number of partitions at most $m$ parts always admits linear congruences.

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MacMahon k 行平面分区的线性代数和全等式

在本文中，我们提供了一种检测 plk(n)（麦克马洪 k 行平面分区数）线性全等的算法，并给出了 k 行平面分区函数的拉马努金式全等不存在的定量结果。我们还证明了 p(n,m)，即最多有 m 个部分的分割数总是允许线性全等。

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.