On the permanents of circulant and degenerate Schur matrices

被引：3

作者：

Kocharovsky, Vitaly V. ^{[1
,2
]}

Kocharovsky, Vladimir V. ^{[2
]}

机构：

[1] Texas A&M Univ, Dept Phys & Astron, College Stn, TX 77843 USA

[2] Russian Acad Sci, Inst Appl Phys, Nizhnii Novgorod 603950, Russia

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2017年 / 519卷

关键词：

Permanent; Degenerate Schur matrix; Circulant matrix; Multiset partition; q-function; Ising model;

D O I：

10.1016/j.laa.2017.01.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We communicate three formulas for the permanents of degenerate Schur and circulant matrices. These combinatorial and integral formulas are intended for the analytical and asymptotic evaluation of the permanents as well as for the solution of three-dimensional Ising model. The paper's goal is to draw attention to the open fundamental problem of finding the permanents' asymptotics. A solution to this problem would be tremendously important for physics of many-body systems and critical phenomena, as well as for quantum field theory. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：366 / 381

页数：16

共 36 条

[1] A linear-optical proof that the permanent is #P-hard [J].

Aaronson, Scott .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2011, 467 (2136) :3393-3405

[2]

[Anonymous], CARUS MATH MONOGR

[3]

[Anonymous], 1999, STAT PROBLEMS INVOLV

[4]

[Anonymous], 2012, A Comprehensive Treatment of qCalculus

[5]

Bapat Ravindra B., 2007, Math. Stud., V76, P55

[6] AN ENUMERATION PROBLEM FOR A CONGRUENCE EQUATION [J].

BRUALDI, RA ;

NEWMAN, M .

JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS SECTION B-MATHEMATICAL SCIENCES, 1970, B 74 (01) :37-+

[7]

Brualdi RA, 2009, CRC DISCR MATH APPL, P1

[8] An efficient tree decomposition method for permanents and mixed discriminants [J].

Cifuentes, Diego ;

Parrilo, Pablo A. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 493 :45-81

[9]

Drummond P.D., 2016, ARXIV160505796V1QUAN

[10]

Exton H, 1983, q-Hypergeometric Functions and Applications

← 1 2 3 4 →