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Search: id:A064230
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| A064230 |
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Triangle T(n,k) = number of rational (0,1) matrices of rank k (n >= 0, 0 <= k <= n). |
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+0
3
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| 1, 1, 1, 1, 9, 6, 1, 49, 288, 174, 1, 225, 6750, 36000, 22560, 1, 961, 118800, 3159750, 17760600, 12514320, 1, 3969, 1807806, 190071000, 5295204600, 34395777360, 28836612000, 1, 16129, 25316928, 9271660734, 1001080231200, 32307576315840
(list; table; graph; listen)
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OFFSET
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0,5
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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.
Table 3 from M. Zivkovic, Classification of small (0,1) matrices (see link). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 28 2006
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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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LINKS
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M. Zivkovic, Classification of small (0,1) matrices, Linear Algebra and its Applications, 414 (2006), 310-346.
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EXAMPLE
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1; 1,1; 1,9,6; 1,49,288,174; ...
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PROGRAM
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(PARI) T=matrix(5, 5); { for(n=0, 4, mm=matrix(n, n); for(k=0, n, T[1+n, 1+k]=0); forvec(x=vector(n*n, i, [0, 1]), for(i=1, n, for(j=1, n, mm[i, j]=x[i+n*(j-1)])); T[1+n, 1+matrank(mm)]++); for(k=0, n, print1(T[1+n, 1+k], if(k<n, ", ", "; "))); ) }
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CROSSREFS
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Cf. A064231, A000409, A000410, A046747.
Sequence in context: A092732 A021108 A021840 this_sequence A089479 A011219 A019961
Adjacent sequences: A064227 A064228 A064229 this_sequence A064231 A064232 A064233
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KEYWORD
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nonn,nice,tabl
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AUTHOR
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njas, Sep 23 2001
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EXTENSIONS
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More terms and PARI code from Michael Somos, Sep 25, 2001
6 more terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Dec 17 2004
More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 28 2006
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