Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2802

 Title: On the Gibson Bounds over Finite Fields Authors: V. Budrevich, MikhailE. Guterman, Alexander Keywords: PermanentDeterminantFinite FieldsPólya 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. URI: http://hdl.handle.net/10525/2802 ISSN: 1310-6600 Appears in Collections: Volume 38, Number 1-3

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