Inversion (discrete mathematics): Difference between revisions

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Three similar vectors are in use that condense the inversions of a permutation into a vector that uniquely determines it. They are often called ''inversion vector'' or ''[[Lehmer code]]''. (A list of sources is found [[v:Inversion (discrete mathematics)#Sources|here]].)

This article uses the term ''inversion vector'' (<math>v</math>) like [[Wolfram Mathematica|Wolfram]].<ref>{{MathWorldWeisstein, |title=Eric W. [http://mathworld.wolfram.com/InversionVector.html "Inversion Vector}}"] From [[MathWorld]]--A Wolfram Web Resource</ref> The remaining two vectors are sometimes called ''left'' and ''right inversion vector'', but to avoid confusion with the inversion vector this article calls them ''left inversion count'' (<math>l</math>) and ''right inversion count'' (<math>r</math>). Interpreted as a [[factorial number system|factorial number]] the left inversion count gives the permutations reverse colexicographic,<ref>Reverse colex order of finitary permutations {{OEIS|A055089}}</ref> and the right inversion count gives the lexicographic index.

[[File:Inversion example; Rothe 1.svg|thumb|Rothe diagram]]