The factorization of the permanent of a matrix with minimal rank in prime characteristic

David Glynn

doi:10.1007/s10623-011-9501-5

The factorization of the permanent of a matrix with minimal rank in prime characteristic

David Glynn

Research output: Contribution to journal › Article › peer-review

Abstract

It is known that any square matrix A of size n over a field of prime characteristic p that has rank less than n/(p - 1) has a permanent that is zero. We give a new proof involving the invariant X _p . There are always matrices of any larger rank with non-zero permanents. It is shown that when the rank of A is exactly n/(p - 1), its permanent may be factorized into two functions involving X _p .

Original language	English
Pages (from-to)	175-177
Number of pages	3
Journal	Designs Codes and Cryptography
Volume	62
Issue number	2
DOIs	https://doi.org/10.1007/s10623-011-9501-5
Publication status	Published - Feb 2012

Keywords

Matrix
Permanent
Prime characteristic
Rank

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10.1007/s10623-011-9501-5

Cite this

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abstract = "It is known that any square matrix A of size n over a field of prime characteristic p that has rank less than n/(p - 1) has a permanent that is zero. We give a new proof involving the invariant X p . There are always matrices of any larger rank with non-zero permanents. It is shown that when the rank of A is exactly n/(p - 1), its permanent may be factorized into two functions involving X p .",

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AB - It is known that any square matrix A of size n over a field of prime characteristic p that has rank less than n/(p - 1) has a permanent that is zero. We give a new proof involving the invariant X p . There are always matrices of any larger rank with non-zero permanents. It is shown that when the rank of A is exactly n/(p - 1), its permanent may be factorized into two functions involving X p .

KW - Matrix

KW - Permanent

KW - Prime characteristic

KW - Rank

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ER -

The factorization of the permanent of a matrix with minimal rank in prime characteristic

Abstract

Keywords

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