Alder-type partition inequality at the general level

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-07-17 DOI:10.1016/j.disc.2024.114157

引用次数: 0

Abstract

A known Alder-type partition inequality of level a, which involves the second Rogers–Ramanujan identity when the level a is 2, states that the number of partitions of n into parts differing by at least d with the smallest part being at least a is greater than or equal to that of partitions of n into parts congruent to $\pm a (\mod d + 3)$ , excluding the part $d + 3 - a$ . In this paper, we prove that for all values of d with a finite number of exceptions, an arbitrary level a Alder-type partition inequality holds without requiring the exclusion of the part $d + 3 - a$ in the latter partition.

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一般水平上的阿尔达型分割不等式

一个已知的 a 级 Alder 型分割不等式（当 a 级为 2 时涉及第二个 Rogers-Ramanujan 特性）指出，将 n 分割成相差至少 d 且最小部分至少为 a 的部分的个数，大于或等于将 n 分割成与±a(modd+3)全等的部分的个数，但不包括 d+3-a 部分。在本文中，我们证明了对于所有 d 值（只有有限个例外），任意水平的 Alder 型分割不等式成立，而不要求在后一个分割中排除 d+3-a 部分。

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.