On the Pólya Conversion Problem for Permanents and Determinants

A. Guterman

doi:10.1007/s10958-014-1762-x

On the Pólya Conversion Problem for Permanents and Determinants

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

Abstract

Let F be a finite field of characteristics different from 2. We show that no bijective map transforms the permanent to the determinant when the cardinality of F is sufficiently large. Also we determine Gibson barriers (the maximal and minimal numbers of nonzero elements) for convertible (0, 1)-matrices and solve several related problems in different matrix subspaces. Our results are illustrated by examples. This paper is based on the joint work with G. Dolinar, B. Kuzma, and M. Orel.

Original language	English
Pages (from-to)	782-786
Number of pages	5
Journal	Journal of Mathematical Sciences
Volume	197
Issue number	6
DOIs	https://doi.org/10.1007/s10958-014-1762-x
State	Published - Mar 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/s10958-014-1762-x

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title = "On the P{\'o}lya Conversion Problem for Permanents and Determinants",

abstract = "Let F be a finite field of characteristics different from 2. We show that no bijective map transforms the permanent to the determinant when the cardinality of F is sufficiently large. Also we determine Gibson barriers (the maximal and minimal numbers of nonzero elements) for convertible (0, 1)-matrices and solve several related problems in different matrix subspaces. Our results are illustrated by examples. This paper is based on the joint work with G. Dolinar, B. Kuzma, and M. Orel.",

author = "A. Guterman",

note = "Funding Information: Acknowledgements. This research was partially supported by the joint Slovene–Russian grant BI-RU/10-11-010 and by the Russian Foundation for Basic Research (project No. 09–01–00303).",

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N2 - Let F be a finite field of characteristics different from 2. We show that no bijective map transforms the permanent to the determinant when the cardinality of F is sufficiently large. Also we determine Gibson barriers (the maximal and minimal numbers of nonzero elements) for convertible (0, 1)-matrices and solve several related problems in different matrix subspaces. Our results are illustrated by examples. This paper is based on the joint work with G. Dolinar, B. Kuzma, and M. Orel.

AB - Let F be a finite field of characteristics different from 2. We show that no bijective map transforms the permanent to the determinant when the cardinality of F is sufficiently large. Also we determine Gibson barriers (the maximal and minimal numbers of nonzero elements) for convertible (0, 1)-matrices and solve several related problems in different matrix subspaces. Our results are illustrated by examples. This paper is based on the joint work with G. Dolinar, B. Kuzma, and M. Orel.

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DO - 10.1007/s10958-014-1762-x

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EP - 786

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

IS - 6

ER -

On the Pólya Conversion Problem for Permanents and Determinants

Abstract

All Science Journal Classification (ASJC) codes

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