The term combinatorial Gray code was introduced in 1980 to refer to any method for generating combinatorial objects so that successive objects differ in some pre-specified, small way. This notion generalizes the classical binary reflected Gray code scheme for listing n-bit binary numbers so that successive numbers differ in exactly one bit position, as well as work in the 1960’s and 70’s on min...

This column will publish short (from just a few paragraphs to ten or so pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathematics pedagogy. They could also include puzzles or brain-teasers involving the use of computers or computational theor...

In the 21 century our society is becoming more and more dependent on software systems. The safety of these systems and the quality of our lives is increasingly dependent on the quality of such systems. A key element in the manufacture and quality assurance process in software engineering is the testing of software and hardware systems. The construction of efficient combinatorial covering suites...

Combinatorial Optimization is a branch of optimization in applied mathematics and computer science, related to operations research, algorithm theory and computational complexity theory that sits at the intersection of many fields, such as artificial intelligence,mathematics and software engineering. Combinatorial optimization problems commonly imply finding values to a set of variables which ar...

The conceptual position of the research is that integration mathematical and chess game activities ensures effective development cognitive intellectual abilities students, motivation to study mathematics, productive its “problem areas”. A technology for identifying correcting zone” based on a has been developed. All stages are presented example mastering complex educational construct-combinator...

The presented material is devoted to the long-term experiment on introduction of computer technologies in process teaching students technical (and not only technical) specialties and lectors various courses disciplines at MAI. was carried out completely different courses, such as: combinatorial analysis, operations research, computational mathematics, as well course information technology, desi...

Recent advances in graph theory, linear algebra, and commutative algebra render us to tackle problems one bough of mathematics with assistance guidance from others. We will elaborate foremost conceptually fathomless homological invariants inextricably linked circulant matrices cycles through various path lengths this article, as well a class Koszul which portrays combinatorial correlation, the ...

In reverse mathematics, one formalizes theorems of ordinary mathematics in second order arithmetic and attempts to discover which set theoretic axioms are required to prove these theorems. Often, this project involves making choices between classically equivalent definitions for the relevant mathematical concepts. In this paper, we consider a number of equivalent definitions for the notions of ...

Paul Erdős (26 March 1913 20 September 1996) was a mathematician par excellence whose results and initiatives have had a large impact and made a strong imprint on the doing of and thinking about mathematics. A mathematician of alacrity, detail, and collaboration, Erdős in his six decades of work moved and thought quickly, entertained increasingly many parameters, and wrote over 1500 articles, t...

The distribution of eigenvalues and the upper bounds for spread interval matrices are significant in various fields mathematics applied sciences, including linear algebra, numerical analysis, control theory, combinatorial optimization. We present within determine their using Geršgorin’s theorem. Specifically, through an equality variance a discrete random variable, we derive symmetric matrices....