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Title: On the Gibson Bounds over Finite Fields
Authors: V. Budrevich, Mikhail
E. Guterman, Alexander
Keywords: Permanent
Finite Fields
Pólya Problem
Issue Date: 2012
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 38, No 1-3, (2012), 395p-416p
Abstract: 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.
Description: 2010 Mathematics Subject Classification: 15A15, 15A04.
ISSN: 1310-6600
Appears in Collections:Volume 38, Number 1-3

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