On the Gibson Bounds over Finite Fields

V. Budrevich, Mikhail, and E. Guterman, Alexander. "On the Gibson Bounds over Finite Fields." Serdica Mathematical Journal 38.1-3 (2012): 395-416. <http://eudml.org/doc/288275>.

@article{V2012,
abstract = {2010 Mathematics Subject Classification: 15A15, 15A04.We investigate the Pólya problem on the sign conversion between the permanent and the determinant over finite fields. The main attention is given to the sufficient conditions which guarantee non-existence of sing-conversion. In addition we show that F3 is the only field with the property that any matrix with the entries from the field is convertible. As a result we obtain that over finite fields there are no analogs of the upper Gibson barrier for the conversion and establish the lower convertibility barrier.* The work on this project is partially supported by the grants MD-2502.2012.1 and RFBR 12-01-00140.},
author = {V. Budrevich, Mikhail, E. Guterman, Alexander},
journal = {Serdica Mathematical Journal},
keywords = {Permanent; Determinant; Finite Fields; Pólya Problem},
language = {eng},
number = {1-3},
pages = {395-416},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On the Gibson Bounds over Finite Fields},
url = {http://eudml.org/doc/288275},
volume = {38},
year = {2012},
}

TY - JOUR
AU - V. Budrevich, Mikhail
AU - E. Guterman, Alexander
TI - On the Gibson Bounds over Finite Fields
JO - Serdica Mathematical Journal
PY - 2012
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 38
IS - 1-3
SP - 395
EP - 416
AB - 2010 Mathematics Subject Classification: 15A15, 15A04.We investigate the Pólya problem on the sign conversion between the permanent and the determinant over finite fields. The main attention is given to the sufficient conditions which guarantee non-existence of sing-conversion. In addition we show that F3 is the only field with the property that any matrix with the entries from the field is convertible. As a result we obtain that over finite fields there are no analogs of the upper Gibson barrier for the conversion and establish the lower convertibility barrier.* The work on this project is partially supported by the grants MD-2502.2012.1 and RFBR 12-01-00140.
LA - eng
KW - Permanent; Determinant; Finite Fields; Pólya Problem
UR - http://eudml.org/doc/288275
ER -