圆柱形分区的麦克马洪分析视图。

IF 0.7 3区数学 Q3 MATHEMATICS

Ramanujan Journal Pub Date : 2025-01-01 Epub Date: 2025-09-22 DOI:10.1007/s11139-025-01225-0

Runqiao Li, Ali K Uncu

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引用次数: 0

摘要

本文用MacMahon划分分析方法研究了两元剖面的圆柱分区。首先利用分格分析找到递归式，然后求解，得到了圆柱分格数生成函数的显式公式。我们还注意到与这些对象相关的一些q级数恒等式，它们显示出某些交替级数的明显的正性质。我们推广了已证明的恒等式，并推测了与Foda-Quano的改进相伴随的Andrews-Gordon恒等式和Bressoud恒等式的新的多项式改进。最后，利用贝利引理的一个变体，我们给出了多项式恒等式的许多新的无限层次。补充信息：在线版本包含补充资料，提供地址为10.1007/s11139-025-01225-0。

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A MacMahon analysis view of cylindric partitions.

We study cylindric partitions with two-element profiles using MacMahon's partition analysis. We find explicit formulas for the generating functions of the number of cylindric partitions by first finding the recurrences using partition analysis and then solving them. We also note some q-series identities related to these objects that show the manifestly positive nature of some alternating series. We generalize the proven identities and conjecture new polynomial refinements of Andrews-Gordon and Bressoud identities, which are companion to Foda-Quano's refinements. Finally, using a variant of the Bailey lemma, we present many new infinite hierarchies of polynomial identities.

Supplementary information: The online version contains supplementary material available at 10.1007/s11139-025-01225-0.

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来源期刊

Ramanujan Journal 数学-数学

CiteScore

1.40

自引率

14.30%

发文量

133

审稿时长

6-12 weeks

期刊介绍： The Ramanujan Journal publishes original papers of the highest quality in all areas of mathematics influenced by Srinivasa Ramanujan. His remarkable discoveries have made a great impact on several branches of mathematics, revealing deep and fundamental connections. The following prioritized listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interest: Hyper-geometric and basic hyper-geometric series (q-series) * Partitions, compositions and combinatory analysis * Circle method and asymptotic formulae * Mock theta functions * Elliptic and theta functions * Modular forms and automorphic functions * Special functions and definite integrals * Continued fractions * Diophantine analysis including irrationality and transcendence * Number theory * Fourier analysis with applications to number theory * Connections between Lie algebras and q-series.