Whitney numbers of rank-metric lattices and code enumeration

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-07-23 DOI:10.1016/j.aam.2025.102938

Giuseppe Cotardo , Alberto Ravagnani , Ferdinando Zullo

引用次数: 0

Abstract

We investigate the Whitney numbers of the first kind of rank-metric lattices, which are closely linked to the open problem of enumerating rank-metric codes having prescribed parameters. We apply methods from the theory of hyperovals and linear sets to compute these Whitney numbers for infinite families of rank-metric lattices. As an application of our results, we prove asymptotic estimates on the density function of certain rank-metric codes that have been conjectured in previous work.

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秩-度量格的惠特尼数与码枚举

我们研究了第一类秩-度量格的Whitney数，它与具有规定参数的秩-度量码的枚举问题密切相关。我们应用超椭圆理论和线性集的方法来计算无限秩-度量格族的这些惠特尼数。作为我们的结果的一个应用，我们证明了在以前的工作中推测的某些秩-度量码的密度函数的渐近估计。

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

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.