On the permanents of circulant and degenerate Schur matrices

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...

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Bibliographic Details
Published in:Linear algebra and its applications 2017-04, Vol.519, p.366-381
Main Authors: Kocharovsky, Vitaly V., Kocharovsky, Vladimir V.
Format: Article
Language:English
Subjects:
Asymptotic methods
Circulant matrix
Combinatorial analysis
Critical phenomena
Degenerate Schur matrix
Field theory
Ising model
Linear algebra
Multiset partition
Permanent
q-function
Quantum field theory
Quantum theory
Theoretical physics
Three dimensional models
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Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2017.01.024