Inversion Number

In determinant expansion by minors, the minimal number of transpositions of adjacent columns in a square matrix needed to turn the matrix representing a permutation of {1,2,...,n} into the identity matrix.

See also

Determinant Expansion by Minors, Transposition

Explore with Wolfram|Alpha


Bressoud, D. and Propp, J. "How the Alternating Sign Matrix Conjecture was Solved." Not. Amer. Math. Soc. 46, 637-646.Conlon, M. M.; Falidas, M.; Forde, M. J.; Kennedy, J. W.; McIlwaine, S.; and Stern, J. "Inversion Numbers of Graphs." Graph Th. Notes New York 37, 42-48, 1999.Cowen, R.; Hechler, S. H.; Kennedy, J. W.; and Ryba, A. "Inversion and Neighborhood Inversion in Graphs." Graph Th. Notes New York 37, 37-41, 1999.

Referenced on Wolfram|Alpha

Inversion Number

Cite this as:

Weisstein, Eric W. "Inversion Number." From MathWorld--A Wolfram Web Resource.

Subject classifications