login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A013588 Smallest positive integer not the determinant of an n X n 0-1 matrix. 6
2, 2, 3, 4, 6, 10, 19, 41, 103, 269 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This majorizes the sequence of maximal determinants only up to the 6th term. It is conjectured that the sequence of maximal determinants majorizes this for all later terms. The 8th term has not been independently verified.

REFERENCES

R. Craigen, The Range of the Determinant Function on the Set of n X n (0,1)-Matrices, J. Combin. Math. Combin. Computing, 8 (1990) pp. 161-171.

Miodrag Zivkovic, Massive computation as a problem solving tool. In Proceedings of the 10th Congress of Yugoslav Mathematicians (Belgrade, 2001), pages 113-128. Univ. Belgrade Fac. Math., Belgrade, 2001.

LINKS

Table of n, a(n) for n=1..10.

W. P. Orrick, The maximal {-1, 1}-determinant of order 15.

G. R. Paseman, A Different Approach to Hadamard's Maximum Determinant Problem

G. R. Paseman, Related Material

M. Zivkovic, Classification of small (0,1) matrices

Index entries for sequences related to binary matrices

Index entries for sequences related to maximal determinants

EXAMPLE

There is no 3 X 3 0-1 matrix with determinant 3, as such a matrix must have a row with at least one 0 in it.

CROSSREFS

Cf. A003432.

Sequence in context: A284908 A103599 A032245 * A108150 A066015 A065482

Adjacent sequences:  A013585 A013586 A013587 * A013589 A013590 A013591

KEYWORD

nice,hard,nonn

AUTHOR

Gerhard R. Paseman (paseman(AT)prado.com)

EXTENSIONS

Extended by William Orrick, Jan 12 2006. a(7), a(8) and a(9) computed by Miodrag Zivkovic. a(7) and a(8) independently confirmed by Antonis Charalambides. a(10) computed by William Orrick. Lower bounds: a(11) >= 739, a(12) >= 2173, a(13) >= 6739, a(14) >= 21278, a(15) >= 69259, a(16) >= 230309

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 14 00:21 EST 2017. Contains 295976 sequences.