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A174638
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Number of n X n (0,1) matrices with two 1's in each row and permanent equal to 8.
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0
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0, 0, 0, 0, 0, 1350, 529200, 172872000, 58352555520, 21677788944000, 9059008787136000, 4286753834515891200, 2297335836334687948800, 1390520517156693315993600, 946759961227258909995264000
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OFFSET
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1,6
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COMMENTS
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If a (0,1) matrix with two 1's in each row has positive permanent, then it equals to a power of 2.
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1967, Ch.4, 66-79.
V. S. Shevelev, On the permanent of the stochastic (0,1)-matrices with equal row sums, Izvestia Vuzov of the North-Caucasus region, Nature sciences 1 (1997), 21-38 (in Russian)
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LINKS
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FORMULA
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In general, for m>=1: number of n X n (0,1) matrices with two 1's in each row the permanent of which equals 2^m is n!*n^(n-1)*2^(-m)*Sum{k=2,...,n}kn^(-k)*C(n,k)*d(k,m), where d(k,m) are associated Stirling numbers of the first kind (see Riordan, p. 75).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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