### Journals Information

**
Mathematics and Statistics Vol. 9(6), pp. 889 - 898 DOI: 10.13189/ms.2021.090604 Reprint (PDF) (483Kb) **

## The Combinatorial Expressions and Probability of Random Generation of Binary Palindromic Digit Combinations

**Vladislav V. Lyubimov ^{*}**

Department of Further Mathematics, Samara University, Samara, Russia

**ABSTRACT**

The aim of this paper is to obtain three types of expressions for calculating the probability of implementing palindromic digit combinations on a finite equally possible combination of zeros and ones. When calculating the probability of implementation of palindromic digit combinations, the classical definition of probability is applied. The main results of the paper are formulated in the form of three theorems. Moreover, the consequences of these theorems and typical examples of calculating the probability of implementing palindromic digit combinations in a data string of binary code are considered. All formulated theorems and their consequences are accompanied by proofs. The obtained numerical results of the paper can be used in the analysis of numerical computer data written as a binary code string in BIN format files. It should also be noted that the combinatorial expressions described in the article for calculating the number of palindromic combinations of digits in the binary number system can be used in number theory and in various branches of computer science. The development of these results from the point of view of obtaining an expression for calculating the number of palindromic combinations of digits in the binary number system contained in two-dimensional data arrays is also of immediate theoretical and practical interest. However, these results are not presented in this work, but they can be considered in subsequent publications.

**KEYWORDS**

Palindromic Digit Combinations, Probability, Binary Number System, Computer Data

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Vladislav V. Lyubimov , "The Combinatorial Expressions and Probability of Random Generation of Binary Palindromic Digit Combinations," Mathematics and Statistics, Vol. 9, No. 6, pp. 889 - 898, 2021. DOI: 10.13189/ms.2021.090604.

(b). APA Format:

Vladislav V. Lyubimov (2021). The Combinatorial Expressions and Probability of Random Generation of Binary Palindromic Digit Combinations. Mathematics and Statistics, 9(6), 889 - 898. DOI: 10.13189/ms.2021.090604.