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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2026. Vol 57

Concatenations of Linear Orderings and Their Rigidity Characteristics

Author(s)

Beibut Sh. Kulpeshov1,2, Sergey V. Sudoplatov3

1 Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

2 Kazakh British Technical University, Almaty, Kazakhstan

3 Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russian Federation

Abstract
Among algebraic operations the operation of concatenation for families of words and for orderings is broadly used in various fields of theoretical and applied mathematics, and informatics. It allows to structure to group and to modify information relative required sequences. Degrees of rigidity are considered as a measures of the mobility of a structure with respect to both the automorphism group and definable closures. Classifying structures with respect to rigidity characteristics allows us to determine the dynamic capabilities of the structure when certain elements are fixed. By examining and describing the degrees of rigidity of concatenations of linear orders, we can both classify these concatenations and establish their diversity. We introduce a series of notions relative degrees of rigidity varying their possibilities from absolute rigidity till nowhere almost rigidity, somewhere non-almost rigidity, and absolute finite non-rigidity. These variations of rigidity characteristics are both described and classified for concatenations of linear orderings. We represent a classification of absolutely rigid linear orderings, describe all linear orderings whose all rigidity characteristics equal 1, and describe possibilities of rigidity characteristics for arbitrary concatenations of countable linear orderings.
About the Authors

Beibut Sh. Kulpeshov, Dr. Sci. (Phys.-Math.), Prof., Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan, kulpesh@mail.ru; Kazakh British Technical University, Almaty, 050000, Kazakhstan, b.kulpeshov@kbtu.kz

Sergey V. Sudoplatov, Dr. Sci. (Phys.–Math.), Prof., Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation, sudoplat@math.nsc.ru

For citation
Kulpeshov B. Sh., Sudoplatov S. V. Concatenations of Linear Orderings and Their Rigidity Characteristics. The Bulletin of Irkutsk State University. Series Mathematics, 2026, vol. 57, pp. 96–112. https://doi.org/10.26516/1997-7670.2026.57.96
Keywords
linear ordering, concatenation, degree of rigidity
UDC
510.67
MSC
03C50, 03C30, 03C64
DOI
https://doi.org/10.26516/1997-7670.2026.57.96
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