A180345 Lexicographically ordered 3X3 matrices containing numbers 1..9 with maximal determinant = 412.

148726593, 157836492, 175429863, 184539762, 249715683, 267935481, 276418953, 294638751, 359814672, 368924571, 386517942, 395627841, 418953276, 429863175, 481267935, 492157836, 517942386, 539762184

Offset: 1

Author

Zak Seidov, Jan 18 2011

Keywords

• nonn
• fini
• base

Comments

The matrices are presented here as 9-digit decimal numbers, one digit per entry in the matrix.

There are exactly 36 such matrices: 148726593, 157836492, 175429863, 184539762, 249715683, 267935481, 276418953, 294638751, 359814672, 368924571, 386517942, 395627841, 418953276, 429863175, 481267935, 492157836, 517942386, 539762184, 571368924, 593148726, 627841395, 638751294, 672359814, 683249715, 715683249, 726593148, 751294638, 762184539, 814672359, 836492157, 841395627, 863175429, 924571368, 935481267, 942386517, 953276418.

Examples

			148726593 => {{1,4,8},{7,2,6},{5,9,3}}:
1 4 8
7 2 6
5 9 3
1*(2*3-9*6)-4(7*3-5*6)+8*(7*9-5*2)=412.
		

Crossrefs

Cf. A085000 Maximal determinant of an n X n matrix using the integers 1 to n^2.

Cf. A088215 (1/36)*number of ways to express n as the determinant of a 3 X 3 matrix with elements 1..9.