Continuous extensions on Euclidean combinatorial configurations

Oksana Pichugina^a, Sergiy Yakovlev<sup>ba

a</sup> National Aerospace University "Kharkiv Aviation Institute", 17 Chkalova Str., Kharkiv, Ukraine, 61070
^b Lodz University of Technology, 116 Zeromskiego Str., Lodz, Poland, 90924

Abstract: In this paper, we introduce a concept of the Euclidean combinatorial configuration as a mapping of a set of certain objects into a point of Euclidean space. We classify Euclidean combinatorial configurations sets based on their structure and constraints. The proposed typology forms the basis for studying continuous functional representations of combinatorial configurations. Special classes of functional extensions are introduced, their properties are described, and corresponding examples are given.

Keywords and phrases: combinatorial configuration, continuous representation, extensions, combinatorial optimization.

MSC: 90C27, 90C57

Received: 01.10.2018
Accepted: 14.11.2021

Language: English

DOI: 10.56415/basm.y2022.i1.p3

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