从 2-adic 估值角度看过度分区

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-09-06 DOI:10.1007/s00010-024-01117-6

Mircea Merca

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引用次数: 0

摘要

在本文中，我们考虑了整数的 2-adic 估值，并为整数的重叠数的生成函数提供了另一种表示方法。由于这一结果，我们得到了一个新公式和一个新的整数过分区数的组合解释。这个公式意味着某类有限制的分区，我们为此提供了两个拉马努扬式的同余式，并提出了两个无限线性不等式族作为开放问题。在此背景下，我们提出了过分区与有两个堆的 m-Modular Nim 游戏之间的联系。

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Overpartitions in terms of 2-adic valuation

In this paper, we consider the 2-adic valuation of integers and provide an alternative representation for the generating function of the number of overpartitions of an integer. As a consequence of this result, we obtain a new formula and a new combinatorial interpretation for the number of overpartitions of an integer. This formula implies a certain type of partitions with restrictions for which we provide two Ramanujan-type congruences and present as open problems two infinite families of linear inequalities. Connections between overpartitions and the game of m-Modular Nim with two heaps are presented in this context.

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.