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A070322 Number of primitive n X n real (0,1)-matrices. 1
1, 1, 3, 139, 25575, 18077431 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

An n X n nonnegative matrix A is primitive iff every element of A^k is > 0 for some power k. If A is primitive then the power which should have all positive entries is <= n^2 - 2n + 2 (Wielandt).

REFERENCES

Sachkov, V. N. and Tarakanov, V. E., Combinatorics of Nonnegative Matrices. Translations of Mathematical Monographs, 213. American Mathematical Society, Providence, RI, 2002.

Wielandt, H. 1950. Unzerlegbare nicht negativen Matrizen, Math. Z. 52, 642-648.

LINKS

Table of n, a(n) for n=0..5.

S. J. Leon, Linear Algebra with Applications: THE PERRON-FROBENIUS THEOREM

Index entries for sequences related to binary matrices

FORMULA

For asymptotics see Sachkov and Tarakanov.

MATHEMATICA

Table[ it=Partition[ #, n ]&/@IntegerDigits[ Range[ 0, -1+2^n^2 ], 2, n^2 ]; Count [ it, (q_?MatrixQ) /; (Max@@Table[ Min@@Flatten[ MatrixPower[ q, k ] ], {k, 1, n^2-2n+2} ] )>0 ], {n, 1, 4} ]

CROSSREFS

Sequence in context: A030247 A139956 A236193 * A053527 A195632 A152504

Adjacent sequences:  A070319 A070320 A070321 * A070323 A070324 A070325

KEYWORD

nonn,hard,more

AUTHOR

N. J. A. Sloane, Aug 22 2003

EXTENSIONS

Wouter Meeussen computed a(0) through a(4), Aug 22 2003

I. J. Kennedy computed a(0) through a(5), Aug 22 2003

STATUS

approved

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Last modified February 21 10:51 EST 2018. Contains 299390 sequences. (Running on oeis4.)