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 
into the identity
matrix.
Inversion Number
See also
Determinant Expansion by Minors, TranspositionExplore with Wolfram|Alpha
References
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 NumberCite this as:
Weisstein, Eric W. "Inversion Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InversionNumber.html