Elementary derivation of a recently proposed integral representation for permanents
Kacper Zalewski (Jagellonian University, Institute of Nuclear, Physics, Krak\'ow, Poland)
TL;DR
This paper provides an elementary combinatorial derivation of a recent integral representation for permanents, removing the need for the matrix to be invertible in the proof.
Contribution
It offers a new, elementary proof of a recent integral representation for permanents that does not require the invertibility assumption.
Findings
Elementary combinatorial proof of the integral representation.
Removal of the invertibility assumption in the derivation.
Simplification of the proof technique for permanents.
Abstract
A recently proposed integral representation for permanents is rederived using only elementary combinatorics. For this proof the assumption that the matrix, for which the permanent is calculated, has an inverse is not necessary.
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Taxonomy
TopicsMatrix Theory and Algorithms · Mathematics and Applications · Algebraic and Geometric Analysis