Searcharxiv⌕ Search

arXiv subjects

Krasimir Yordzhev

Publications and source records attributed to Krasimir Yordzhev.

At least 19 recordsLinked to original sources
arXiv2026

On some classes of binary matrices

The work considers the set $Λ_n^k$ of all $n\times n$ binary matrices having the same number of $k$ units in each row and each column. The article specifically focuses on the matrices whose rows and columns are sorted lexicographically. We examine some particular cases and special properties of this matrices. Finally, we demonstrate the relationship between the Fibonacci numbers and the cardinality of two classes of $Λ_n^k$-matrices with lexicographically sorted rows and columns.

math.CO↗
arXiv2026

Mathematical Modeling in the Textile Industry

A mathematical model, describing some different weaving structures, is made in this article. The terms self-mirror and rotation-stable weaving structure are initiated here. There are used the properties and operations in the set of the binary matrices and an equivalence relation in this set. Some combinatorial problems about finding the cardinal number and the elements of the factor set according to this relation is discussed. We propose an algorithm, which solves these problems. The presentation of an arbitrary binary matrix using sequence of nonnegative integers is discussed. It is shown that the presentation of binary matrices using ordered n-tuples of natural numbers makes the algorithms faster and saves a lot of memory. Implementing these ideas a computer program, which receives all of the examined objects, is created. In the paper we use object-oriented programming using the syntax and the semantic of C++ programming language. Some advantages in the use of bitwise operations are shown. The results we have received are used to describe the topology of the different weaving structures.

math.GM↗
arXiv2026

On A. V. Anisimov's problem for finding a polynomial algorithm checking inclusion of context-free languages in group languages

The work investigates the problem of whether a context-free language is a subset of a group language. A.~V. Anisimov has shown that the problem of determining the unambiguity of finite automata is a special case of this problem. Then the question of finding polynomial algorithm verifying the inclusion of context-free languages in group languages naturally arises. The article focuses on this open problem. For the purpose, the paper describes an unconventional method of description of context-free languages, namely a representation with the help of a finite digraph whose arcs are labelled with a specially defined monoid $\mathcal{U}$. Also, we define a semiring $\mathcal{S}_\mathcal{U}$ whose elements are the set $2^\mathcal{U}$ of all subsets of $\mathcal{U}$ and with operations - product and union of the elements of $2^\mathcal{U}$. The described algorithm executes no more than $O(n^3)$ operations in $\mathcal{S}_\mathcal{U}$.

cs.FL↗
arXiv2024

On some randomized algorithms and their evaluation

The paper considers implementations of some randomized algorithms in connection with obtaining a random $n^2 \times n^2$ Sudoku matrix with programming language C++. For this purpose we describes the set $Π_n$ of all $(2n) \times n$ matrices, consisting of elements of the set $\mathbb{Z}_n =\{ 1,2,\ldots ,n\}$, such that every row is a permutation. We emphasize the relationship between these matrices and the $n^2 \times n^2$ Sudoku matrices. An algorithm to obtain random $Π_n$ matrices is presented in this paper. Several auxiliary algorithms that are related to the underlying problem have been described. We evaluated all algorithms according to two criteria - probability evaluation, and time for generation of random objects and checking of belonging to a specific set. This evaluations are interesting from both theoretical and practical point of view because they are particularly useful in the analysis of computer programs.

cs.DM↗
arXiv2021

Canonical matrices with entries integers modulo p

The work considers an equivalence relation in the set of all $n\times m$ matrices with entries in the set $[p]=\{ 0,1,\ldots , p-1 \}$. In each element of the factor-set generated by this relation, we define the concept of canonical matrix, namely the minimal element with respect to the lexicographic order. We have found a necessary and sufficient condition for an arbitrary matrix with entries in the set $[p]$ to be canonical. For this purpose, the matrices are uniquely represented by ordered n-tuples of integers.

math.CO↗
arXiv2021

The bitwise operations in relation to the concept of set

We contemplate this article to help the teachers of programming in his aspiration for giving some appropriate and interesting examples. The work will be especially useful for students-future programmers, and for their lecturers. Some of the strong sides of these programming languages C/C++ and Java are the possibilities of low-level programming. Some of the means for this possibility are the introduced standard bitwise operations, with the help of which, it is possible to directly operate with every bit of an arbitrary variable situated in the computers memory. In the current study, we are going to describe some methodical aspects for work with the bitwise operations and we will discuss the benefit of using bitwise operations in programming. The article shows some advantages of using bitwise operations, realizing various operations with sets.

cs.PL↗
arXiv2020

On some representations of context-free languages

Context-free languages are widely used to describe the syntax of programming languages and natural languages. Usually, we describe a context-free language mathematically with the help of context-free grammar (for generation) or pushdown automata (for recognition). The purpose of this study is to describe some unconventional methods of description of context-free languages, namely a representation with the help of finite digraphs and with automata - generators of context-free languages. We will mainly focus on the mathematical models of these representations.

cs.FL↗
arXiv2020

Students Readiness for E-learning in the Universities in Yemen

The e-learning is an advanced version of traditional education. It is defined as a way of learning by using the communication mechanisms of modern computer networks and multimedia, including voice, image, and graphics and mechanisms to search electronic libraries, as well as web portals, whether in the context of distance learning or in the classroom. The people who engage in the transition to web-supported education are the administrative staff, the faculty, and the students. They all have their needs and they all should meet specific requirements in order to facilitate the transition. The article presents the results of questionnaire research of the students readiness for e-learning in Yemeni universities.

cs.CY↗
arXiv2016

On the number of mutually disjoint pairs of S-permutation matrices

This work examines the concept of S-permutation matrices, namely $n^2 \times n^2$ permutation matrices containing a single 1 in each canonical $n \times n$ subsquare (block). The article suggests a formula for counting mutually disjoint pairs of $n^2 \times n^2$ S-permutation matrices in the general case by restricting this task to the problem of finding some numerical characteristics of the elements of specially defined for this purpose factor-set of the set of $n \times n$ binary matrices. The paper describe an algorithm that solves the main problem. To do that, every $n\times n$ binary matrix is represented uniquely as a n-tuple of integers.

math.CO↗
arXiv2016

The bitwise operations in relation to obtaining Latin squares

The main thrust of the article is to provide interesting example, useful for students of using bitwise operations in the programming languages C ++ and Java. As an example, we describe an algorithm for obtaining a Latin square of arbitrary order. We will outline some techniques for the use of bitwise operations.

cs.OH↗
arXiv2016

Canonical binary matrices related to bipartite graphs

The current paper is dedicated to the problem of finding the number of mutually non isomorphic bipartite graphs of the type $g=\langle R_g ,C_g ,E_g \rangle$ at given $n=|R_g |$ and $m=|C_g |$, where $R_g$ and $C_g$ are the two disjoint parts of the vertices of the graphs $g$, and $E_g$ is the set of edges, $Eg \subseteq R_g \times C_g$. For this purpose, the concept of canonical binary matrix is introduced. The different canonical matrices unambiguously describe the different with exactness up to isomorphism bipartite graphs. We have found a necessary and sufficient condition an arbitrary matrix to be canonical. This condition could be the base for realizing recursive algorithm for finding all $n \times m$ canonical binary matrices and consequently for finding all with exactness up to isomorphism binary matrices with cardinality of each part equal to $n$ and $m$.

cs.DM↗
arXiv2016

On an algorithm for receiving Sudoku matrices

This work examines the problem to describe an efficient algorithm for obtaining $n^2 \times n^2$ Sudoku matrices. For this purpose, we define the concepts of $n\times n$ $Π_n$-matrix and disjoint $Π_n$-matrices. The article, using the set-theoretical approach, describes an algorithm for obtaining $n^2$-tuples of $n\times n$ mutually disjoint $Π_n$ matrices. We show that in input $n^2$ mutually disjoint $Π_n$ matrices, it is not difficult to receive a Sudoku matrix.

cs.DS↗
arXiv2016

On an application of multidimensional arrays

This article discusses some difficulties in the implementation of combinatorial algorithms associated with the choice of all elements with certain properties among the elements of a set with great cardinality.The problem has been resolved by using multidimensional arrays. Illustration of the method is a solution of the problem of obtaining one representative from each equivalence class with respect to the described in the article equivalence relation in the set of all $m\sim n$ binary matrices. This equivalence relation has an application in the mathematical modeling in the textile industry.

cs.DS↗
arXiv2015

Semi-canonical binary matrices

In this paper, we define the concepts of semi-canonical and canonical binary matrix. Strictly mathematical, we prove the correctness of these definitions. We describe and we implement an algorithm for finding all semi-canonical binary matrices taking into account the number of 1 in each of them. This problem relates to the combinatorial problem of finding all pairs of disjoint S-permutation matrices. In the described algorithm, the bit-wise operations are substantially used.

math.CO↗
arXiv2015

Calculation of the Number of all Pairs of Disjoint S-permutation Matrices

The concept of S-permutation matrix is considered. A general formula for counting all disjoint pairs of $n^2 \times n^2$ S-permutation matrices as a function of the positive integer $n$ is formulated and proven in this paper. To do that, the graph theory techniques have been used. It has been shown that to count the number of disjoint pairs of $n^2 \times n^2$ S-permutation matrices, it is sufficient to obtain some numerical characteristics of all $n\times n$ bipartite graphs.

math.CO↗
arXiv2014

Number systems and combinatorial problems

The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in combinatorial analysis and most of all when proving some combinatorial identities. To demonstrate discussed in this article method we have chosen several suitable mathematical tasks.

math.HO↗
arXiv2014

On the cardinality of a factor set in the symmetric group

Let $n$ be a positive integer, $σ$ be an element of the symmetric group $\mathcal{S}_n$ and let $σ$ be a cycle of length $n$. The elements $α,β\in \mathcal{S}_n$ are $σ$-equivalent, if there are natural numbers $k$ and $l$, such that $σ^k α=βσ^l$, which is the same as the condition to exist natural numbers $k_1$ and $l_1$, such that $α= σ^{k_1} βσ^{l_1}$. In this work we examine some properties of the so defined equivalence relation. We build a finite oriented graph $Γ_n$ with the help of which is described an algorithm for solving the combinatorial problem for finding the number of equivalence classes according to this relation.

math.CO↗