Schemes of non-sequential pure 5-opt moves

There are exactly 60 pure non-sequential 5-opt move types. As in the case of non-sequential pure 4-opt move types they form two distinct groups. The first group contains 20 moves that consists of completely independent 2-opt and 3-opt moves, changing non-overlaping ranges (for example AbCde, AbcDe). We can see similar types of non-sequential moves among all k-opts where k>=4.

The remaining move types can be divided into two sub-groups, each containing 20 types. All move types in the first sub-group (II.A) have easily noticeable trait. They contain two parallel links close to each other, the same characteristic pattern which occurs in double bridge. This suggests that moves of at least some of these types can be obtained by some simple modifications of double bridge (or crossed bridge). Move types in the second sub-group (II.B) does not have this kind of connections and their possible origin is not so obvious.

All non-sequential pure 5-opt moves

Group I
AbCde	AbcDe	AbCED
AbCEd	AbCeD	AbeDc
ACBDe	ACbDe	AcBDe
ACdEB	ACdEb	AdCbe
AEBcD	AeBcD	AeCdb
AecDb	Aecdb	AEdCb
AeDCb	AeDcB
Group II.A
AbEDC	AbdeC	Acdeb
AceDB	ADbce	ADCBe
ADCeb	ADceB	ADebc
AdebC	ADeCB	AdECB
Aebcd	AEbdC	AebDC
AECbd	AECdB	AEcDB
AEDBc	AEDbC
Group II.B
AbEcd	AcdBe	ACeBd
ACebd	AcEBd	AcEbD
AcebD	AcEDb	AcEdB
ADBec	ADbeC	AdBec
AdbEC	AdbEc	AdCeB
AdEbc	AdeBc	AEbDc
AEcBd	AeCBd