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.
|Number of pages||5|
|Journal||Journal of Mathematical Sciences|
|State||Published - Mar 2014|
Bibliographical noteFunding 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).