Here are the canonicalized partitions generated directly in lexicographic
order:
cnext=:3 : 0
inc=.(2 </\ y)*.}: -. ~: y
if. 0=+/inc do. /:~ y return. end.
last =.inc i: 1
(last {. y), nexts last }. y
)
nexts=:3 : '({.,/:~@:}.) ( y i. <./ @: (#~ (>{.)) y) swap y'
swap=:4 : 'y {~ C. (0,x);<:#y'
cnext^:(i.15) 0 0 1 1 2 2
0 0 1 1 2 2
0 0 1 2 1 2
0 0 1 2 2 1
0 1 0 1 2 2
0 1 0 2 1 2
0 1 0 2 2 1
0 1 1 0 2 2
0 1 1 2 0 2
0 1 1 2 2 0
0 1 2 0 1 2
0 1 2 0 2 1
0 1 2 1 0 2
0 1 2 1 2 0
0 1 2 2 0 1
0 1 2 2 1 0
Best wishes,
John
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