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Permanents of matrices of signed ones

Wanless, IM (2005). Permanents of matrices of signed ones. Linear and Multilinear Algebra,53(6):427-433.

Document type: Journal Article
Citation counts: Scopus Citation Count Cited 4 times in Scopus Article | Citations
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Title Permanents of matrices of signed ones
Author Wanless, IM
Journal Name Linear and Multilinear Algebra
Publication Date 2005
Volume Number 53
Issue Number 6
ISSN 0308-1087   (check CDU catalogue open catalogue search in new window)
Scopus ID 2-s2.0-18844380989
Start Page 427
End Page 433
Total Pages 7
Place of Publication United Kingdom
Publisher Taylor & Francis
HERDC Category C1 - Journal Article (DEST)
Abstract By calculating the permanents for all Hadamard matrices of orders up to and including 28 we answer a problem posed by E.T.H. Wang and a similar question asked by H. Perfect. Both questions are answered by the existence of Hadamard matrices of order 20 which do not seem to be simply related but nevertheless have the same permanent. For orders up to and including 20 we also settle several other existence questions involving permanents of (+1,-1)-matrices. Specifically, we establish the lowest positive value taken by the permanent in these cases and find matrices which have equal permanent and determinant when such a matrix exists. Our results address Conjectures 19 and 36 and Problems 5 and 7 in Minc's well known catalogue of unsolved problems on permanents. We also include a little-known proof that there exists a (+1,-1)-matrix A of order n such that per( A )=0 if and only if n +1 is not a power of 2.
Keywords permanent
hadamard matrix
(1,-1)-matrix
toeplitz matrix
DOI http://dx.doi.org/10.1080/03081080500093990   (check subscription with CDU E-Gateway service for CDU Staff and Students  check subscription with CDU E-Gateway in new window)
 
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Created: Fri, 12 Sep 2008, 08:35:25 CST by Administrator