Exact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix

We present a finite-order system of recurrence relations for the permanent of circulant matrices containing a band of <i>k</i> any-value diagonals on top of a uniform matrix (for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"...

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Autores principales:	Vitaly Kocharovsky, Vladimir Kocharovsky, Vladimir Martyanov, Sergey Tarasov
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	permanent circulant matrix ménage problem NP-hard problem critical phenomena quantum computing Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/f715c6e390a7461a874af18fed4a205e
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spelling	oai:doaj.org-article:f715c6e390a7461a874af18fed4a205e2021-11-25T17:29:32ZExact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix10.3390/e231114231099-4300https://doaj.org/article/f715c6e390a7461a874af18fed4a205e2021-10-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1423https://doaj.org/toc/1099-4300We present a finite-order system of recurrence relations for the permanent of circulant matrices containing a band of <i>k</i> any-value diagonals on top of a uniform matrix (for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></semantics></math></inline-formula> and 3) and the method for deriving such recurrence relations, which is based on the permanents of the matrices with defects. The proposed system of linear recurrence equations with variable coefficients provides a powerful tool for the analysis of the circulant permanents, their fast, linear-time computing; and finding their asymptotics in a large-matrix-size limit. The latter problem is an open fundamental problem. Its solution would be tremendously important for a unified analysis of a wide range of the nature’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>♯</mo><mi>P</mi></mrow></semantics></math></inline-formula>-hard problems, including problems in the physics of many-body systems, critical phenomena, quantum computing, quantum field theory, theory of chaos, fractals, theory of graphs, number theory, combinatorics, cryptography, etc.Vitaly KocharovskyVladimir KocharovskyVladimir MartyanovSergey TarasovMDPI AGarticlepermanentcirculant matrixménage problemNP-hard problemcritical phenomenaquantum computingScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1423, p 1423 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	permanent circulant matrix ménage problem NP-hard problem critical phenomena quantum computing Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	permanent circulant matrix ménage problem NP-hard problem critical phenomena quantum computing Science Q Astrophysics QB460-466 Physics QC1-999 Vitaly Kocharovsky Vladimir Kocharovsky Vladimir Martyanov Sergey Tarasov Exact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix
description	We present a finite-order system of recurrence relations for the permanent of circulant matrices containing a band of <i>k</i> any-value diagonals on top of a uniform matrix (for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></semantics></math></inline-formula> and 3) and the method for deriving such recurrence relations, which is based on the permanents of the matrices with defects. The proposed system of linear recurrence equations with variable coefficients provides a powerful tool for the analysis of the circulant permanents, their fast, linear-time computing; and finding their asymptotics in a large-matrix-size limit. The latter problem is an open fundamental problem. Its solution would be tremendously important for a unified analysis of a wide range of the nature’s <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>♯</mo><mi>P</mi></mrow></semantics></math></inline-formula>-hard problems, including problems in the physics of many-body systems, critical phenomena, quantum computing, quantum field theory, theory of chaos, fractals, theory of graphs, number theory, combinatorics, cryptography, etc.
format	article
author	Vitaly Kocharovsky Vladimir Kocharovsky Vladimir Martyanov Sergey Tarasov
author_facet	Vitaly Kocharovsky Vladimir Kocharovsky Vladimir Martyanov Sergey Tarasov
author_sort	Vitaly Kocharovsky
title	Exact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix
title_short	Exact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix
title_full	Exact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix
title_fullStr	Exact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix
title_full_unstemmed	Exact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix
title_sort	exact recursive calculation of circulant permanents: a band of different diagonals inside a uniform matrix
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/f715c6e390a7461a874af18fed4a205e
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Exact Recursive Calculation of Circulant Permanents: A Band of Different Diagonals inside a Uniform Matrix

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