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.
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页码：366 / 381
页数：16
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