部分间隔有限制的分区的公式和猜想

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-10-07 DOI:10.1016/j.aam.2025.102981

George E. Andrews , Mohamed El Bachraoui

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引用次数: 0

摘要

研究了若干整数分区及其加权类似分区，并对其各部分的间隔条件进行了研究。q-二重级数在为我们的序列生成函数时更为有效。我们给出了这种划分的数目的显式公式，我们导出了涉及整数划分的恒等式，并证明了我们的一些加权序列是正的。进一步，我们对两个q-二重级数的系数提出了两个奇怪的猜想。

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Formulas and conjectures for partitions with restrictions on interval of parts

We focus on certain integer partitions and their weighted analogues with conditions on the interval of their parts. The q-double series turn out to be more fruitful as generating functions for our sequences. We give explicit formulas for the number of such partitions, we derive identities involving integer partitions, and we prove that some of our weighted sequences are positive. Furthermore, we state two curious conjectures on the coefficients of two q-double series.

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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.