On the Unassociated Matrices Number of the n Order and a Given Determinant

The main object of the present work is to derive new relations between the number of n-order non-associated matrices and a determinant N, which can subsequently be put into use. In this study we mainly employ the Hermite triangular form of n-order full matrices and the determinant N. The following n...

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Autors principals:	Pachev, U. M., Пачев, У. М., Dokhov, R. A., Дохов, Р. А.
Format:	Статья
Idioma:	English
Publicat:	2023
Matèries:	Canonical decomposition Upper bound Euler function Unassociated matrices Integer matrix Mobius function Triangular canonical form Recurrence relation Primitive matrix
Accés en línia:	https://dspace.ncfu.ru/handle/20.500.12258/25193
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record_format	dspace
spelling	ir-20.500.12258-251932023-09-07T08:32:33Z On the Unassociated Matrices Number of the n Order and a Given Determinant Pachev, U. M. Пачев, У. М. Dokhov, R. A. Дохов, Р. А. Canonical decomposition Upper bound Euler function Unassociated matrices Integer matrix Mobius function Triangular canonical form Recurrence relation Primitive matrix The main object of the present work is to derive new relations between the number of n-order non-associated matrices and a determinant N, which can subsequently be put into use. In this study we mainly employ the Hermite triangular form of n-order full matrices and the determinant N. The following new results are obtained in the work: 1.formula for σ0(n, p1• ⋯ • pk) n-order non-associated primitive matrices with non-square determinants values N= p1• ⋯ • pk, where pi are primes;2.formula for σ0(n, pα) primitive non-associated n-order matrices N= pα, where p is a prime;3.the recurrent relations is established for σ0(n, N) by order of matrices considered;4.an upper estimate for the number of the considered n order matrices and the determinant is obtained close to the precise value of σ(n, N) in the case where the canonical expansion of N is not given;5.the relationship between σ(n, pα) as well as σ0(n, pα) and the Gaussian coefficients by combinatorics is established. 2023-09-07T08:31:42Z 2023-09-07T08:31:42Z 2023 Статья Pachev, U., Dokhov, R. On the Unassociated Matrices Number of the n Order and a Given Determinant // Lecture Notes in Networks and Systems. - 2023. - 702 LNNS, pp. 146-156. - DOI: 10.1007/978-3-031-34127-4_15 http://hdl.handle.net/20.500.12258/25193 en Lecture Notes in Networks and Systems application/pdf
institution	СКФУ
collection	Репозиторий
language	English
topic	Canonical decomposition Upper bound Euler function Unassociated matrices Integer matrix Mobius function Triangular canonical form Recurrence relation Primitive matrix
spellingShingle	Canonical decomposition Upper bound Euler function Unassociated matrices Integer matrix Mobius function Triangular canonical form Recurrence relation Primitive matrix Pachev, U. M. Пачев, У. М. Dokhov, R. A. Дохов, Р. А. On the Unassociated Matrices Number of the n Order and a Given Determinant
description	The main object of the present work is to derive new relations between the number of n-order non-associated matrices and a determinant N, which can subsequently be put into use. In this study we mainly employ the Hermite triangular form of n-order full matrices and the determinant N. The following new results are obtained in the work: 1.formula for σ0(n, p1• ⋯ • pk) n-order non-associated primitive matrices with non-square determinants values N= p1• ⋯ • pk, where pi are primes;2.formula for σ0(n, pα) primitive non-associated n-order matrices N= pα, where p is a prime;3.the recurrent relations is established for σ0(n, N) by order of matrices considered;4.an upper estimate for the number of the considered n order matrices and the determinant is obtained close to the precise value of σ(n, N) in the case where the canonical expansion of N is not given;5.the relationship between σ(n, pα) as well as σ0(n, pα) and the Gaussian coefficients by combinatorics is established.
format	Статья
author	Pachev, U. M. Пачев, У. М. Dokhov, R. A. Дохов, Р. А.
author_facet	Pachev, U. M. Пачев, У. М. Dokhov, R. A. Дохов, Р. А.
author_sort	Pachev, U. M.
title	On the Unassociated Matrices Number of the n Order and a Given Determinant
title_short	On the Unassociated Matrices Number of the n Order and a Given Determinant
title_full	On the Unassociated Matrices Number of the n Order and a Given Determinant
title_fullStr	On the Unassociated Matrices Number of the n Order and a Given Determinant
title_full_unstemmed	On the Unassociated Matrices Number of the n Order and a Given Determinant
title_sort	on the unassociated matrices number of the n order and a given determinant
publishDate	2023
url	https://dspace.ncfu.ru/handle/20.500.12258/25193
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On the Unassociated Matrices Number of the n Order and a Given Determinant

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