Abstract

In the class of discrete enumeration problems, an important place belongs to the problems of searching for frequently and infrequently occurring elements in integer data. Questions on the effectiveness of such a search are directly related to the study of the metric (quantitative) properties of sets of frequent and infrequent elements. It is assumed that the initial data are presented in the form of an integer matrix, whose rows are descriptions of the studied objects in the given system of the numerical characteristics of these objects, called attributes. The case is considered when each attribute takes values from the set {\(0,1, \ldots ,k - 1\} ,\; k \geqslant 2\). Asymptotic estimates for the typical number of special, frequent fragments of object descriptions, called correct fragments, and estimates for the typical length of such a fragment are given. We also present new results concerning the study of the metric properties of the minimal infrequent fragments of descriptions of objects.

中文翻译：

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整数数据的一些特殊逻辑分析问题的解数

摘要

在一类离散枚举问题中，一个重要的地方是在整数数据中搜索频繁和不频繁出现的元素的问题。关于这种搜索的有效性的问题与频繁和不频繁元素集的度量（定量）属性的研究直接相关。假设初始数据以整数矩阵的形式呈现，其行是给定系统中研究对象的描述，这些对象的数值特征称为属性。当每个属性从集合 { \(0,1, \ldots ,k - 1\} ,\; k \geqslant 2\) 中获取值时，会考虑这种情况。给出了对对象描述的特殊、频繁片段（称为正确片段）的典型数量的渐近估计，以及对此类片段的典型长度的估计。我们还提出了有关对象描述的最小不频繁片段的度量属性研究的新结果。