ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)
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9
Issue
vol 63 / September, 2020
Article

DOI 10.17586/0021-3454-2015-58-6-436-442

UDC 681.3.053, 681.3.06

APPLICATION OF FACTORIAL SYSTEM TO COMBINATORIAL PROBLEMS SOLVING

V. I. Polyakov
ITMO University, Saint Petersburg, 197101, Russian Federation; Associate Professor


V. I. Skorubskiy
Saint Petersburg National Research University of Information Technologies, Mechanics and Optics; State Polytechnic University; Associate professor


Y. V. Ekalo
St. Petersburg Electro-Technical University, Research and Engineering Center OJSC; Associate Professor; Director General


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Abstract. Properties of the factorial number system are analyzed and several new fields of its application to combinatorial problems in programming and computer systems design are considered. Factorial numbers may be univalently enumerated with decimal or binary integers and interpreted as permutations of elements of any type. Decoding of binary-coded record of permutation in the factorial number system makes it possible to relate each permutation to a unique distribution of discreet objects (elements, references, etc.) in a specific discreet space. Permutations and distributions may be used in solving the problems of automation of design and commutation of calculating system channels, as well as in data protection.
Keywords: permutations, factorial number system, binary coding of factorial numbers, transformation of binary number into a factorial one and back, distributions, combinations of elements