On some questions concerning permanents of (1,−1)-matrices
On some questions concerning permanents of (1,−1)-matrices
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关于(1,−1)-矩阵常量的一些问题
DOI：
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发表时间：
1983
期刊：
影响因子：
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通讯作者：
N. Seifter
中科院分区：
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作者：
Arnold R. Kräuter;N. Seifter
Let Ωn denote the set of alln×n-(1,−1)-matrices. E.T.H. Wang has posed the following problem: For eachn≧4, can one always find nonsingularA∈Ωn such that |perA|=|detA| (*)? We present a solution forn≦6 and, more generally, we show that (*) does not hold ifn=2k−1,k≧2, even for singularA∈Ωn. Moreover, we prove that perA≠0 ifA∈Ωn,n=2k−1, and we derive new results concerning the divisibility of the permanent in Ωn by powers of 2.
