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Search: id:A064231
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| A064231 |
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Triangle read by rows: T(n,k) = number of rational (+1,-1) matrices of rank k (n >= 1, 1 <= k <= n). |
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+0
3
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| 2, 8, 8, 32, 288, 192, 128, 6272, 36864, 22272, 512, 115200, 3456000, 18432000, 11550720, 2048, 1968128, 243302400, 6471168000, 36373708800, 25629327360, 8192, 32514048, 14809546752, 1557061632000, 43378316083200, 281770208133120
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Rows add to 2^(n^2).
Komlos and later Kahn, Komlos and Szemeredi show that almost all such matrices are invertible.
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REFERENCES
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J. Kahn, J. Komlos and E. Szemeredi: On the probability that a random +-1 matrix is singular, J. AMS 8 (1995), 223-240.
J. Komlos, On the determinants of random matrices, Studia Sci. Math. Hungar., 3 (1968), 387-399.
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EXAMPLE
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2; 8,8; 32,288,192; 128,6272,36864,22272; ...
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PROGRAM
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(PARI) T=matrix(4, 4); { for(n=1, 4, mm=matrix(n, n); for(k=1, n, T[n, k]=0); forvec(x=vector(n*n, i, [0, 1]), for(i=1, n, for(j=1, n, mm[i, j]=(-1)^x[i+n*(j-1)])); T[n, matrank(mm)]++); for(k=1, n, print1(T[n, k], if(k<n, ", ", "; "))); ) }
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CROSSREFS
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Cf. A064230, A000409, A000410, A046747.
Sequence in context: A093907 A116471 A146749 this_sequence A156052 A083523 A009181
Adjacent sequences: A064228 A064229 A064230 this_sequence A064232 A064233 A064234
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KEYWORD
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nonn,nice,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Sep 23 2001
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EXTENSIONS
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More terms and PARI code from Michael Somos, Sep 25, 2001
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 02 2006
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