A Structure of the Ensemble of Integer Vectors on the Multidimensional Sphere

УДК 514.742.2+519.23

  • S.V. Dronov Altai State University (Barnaul, Russia) Email: dsv@math.asu.ru
  • A.S. Petrikov Altai State Medical University (Barnaul, Russia) Email: petricov_alex@mail.ru
DOI_disc_logo https://doi.org/10.14258/izvasu(2020)1-13
Keywords: integer vectors, multidimensional combinatorial geometry, rank coefficients, significance of correlations

Abstract

This paper studies the mutual arrangements of multidimensional vectors with coordinates that are consecutive natural numbers and the maximum of which coincides with the dimension of the corresponding Euclidean space. The set of all such vectors is called an ensemble of integer vectors. Since the membership of a vector in an ensemble means that its coordinates are some permutation of coordinates of any other vectors of the ensemble, all these vectors have the same length and, when they are placed at the origin, all their ends are lying on a sphere with a radius equal to this length. The vector (1, 2, ..., n) is considered as the main vector of the ensemble. All possible angles that can be formed by the vectors of an integer ensemble are studied. In particular, authors are looking for the number of those that form angles of equal magnitude with the main vector. Obtained results can be used in the construction of the exact distribution of the rank correlation coefficient. In conclusion, the application of this distribution to one of the problems of differential diagnosis in the analysis of deep vein thrombosis and pulmonary artery thromboembolism is considered.

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Author Biographies

S.V. Dronov, Altai State University (Barnaul, Russia)

кандидат физико-математических наук, доцент кафедры математического анализа

A.S. Petrikov, Altai State Medical University (Barnaul, Russia)

доктор медицинских наук, профессор кафедры факультетской хирургии, госпитальной хирургии с курсом хирургии дополнительного профессионального образования

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Published
2020-03-06
How to Cite
Dronov S., Petrikov A. A Structure of the Ensemble of Integer Vectors on the Multidimensional Sphere // Izvestiya of Altai State University, 2020, № 1(111). P. 83-88 DOI: 10.14258/izvasu(2020)1-13. URL: https://izvestiya.asu.ru/article/view/%282020%291-13.
Issue
No 1(111) (2020): Izvestiya of Altai State University
Section
Математика и механика

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