* Joerg Arndt <arndt@jjj.de> [Jan 30. 2012 13:32]:
[...]
Subset-lex alone can be quite cool, here's for the Catalan restricted growth strings: 1: [ . . . . 1 ] 4 ()()()(()) 1.1.1.11.. 2: [ . . . 1 2 ] 4 ()()((())) 1.1.111... 3: [ . . . 1 1 ] 4 ()()(()()) 1.1.11.1.. 4: [ . . . 1 . ] 3 ()()(())() 1.1.11..1. 5: [ . . 1 . 1 ] 4 ()(())(()) 1.11..11.. 6: [ . . 1 1 2 ] 4 ()(()(())) 1.11.11... 7: [ . . 1 1 1 ] 4 ()(()()()) 1.11.1.1.. 8: [ . . 1 2 3 ] 4 ()(((()))) 1.1111.... 9: [ . . 1 2 2 ] 4 ()((()())) 1.111.1... 10: [ . . 1 2 1 ] 4 ()((())()) 1.111..1.. 11: [ . . 1 2 . ] 3 ()((()))() 1.111...1. 12: [ . . 1 1 . ] 3 ()(()())() 1.11.1..1. 13: [ . . 1 . . ] 2 ()(())()() 1.11..1.1. 14: [ . 1 . . 1 ] 4 (())()(()) 11..1.11.. 15: [ . 1 . 1 2 ] 4 (())((())) 11..111... 16: [ . 1 . 1 1 ] 4 (())(()()) 11..11.1.. 17: [ . 1 . 1 . ] 3 (())(())() 11..11..1. 18: [ . 1 1 . 1 ] 4 (()())(()) 11.1..11.. 19: [ . 1 1 1 2 ] 4 (()()(())) 11.1.11... 20: [ . 1 1 1 1 ] 4 (()()()()) 11.1.1.1.. 21: [ . 1 1 2 3 ] 4 (()((()))) 11.111.... 22: [ . 1 1 2 2 ] 4 (()(()())) 11.11.1... 23: [ . 1 1 2 1 ] 4 (()(())()) 11.11..1.. 24: [ . 1 1 2 . ] 3 (()(()))() 11.11...1. 25: [ . 1 1 1 . ] 3 (()()())() 11.1.1..1. 26: [ . 1 2 . 1 ] 4 ((()))(()) 111...11.. 27: [ . 1 2 1 2 ] 4 ((())(())) 111..11... 28: [ . 1 2 1 1 ] 4 ((())()()) 111..1.1.. 29: [ . 1 2 2 3 ] 4 ((()(()))) 111.11.... 30: [ . 1 2 2 2 ] 4 ((()()())) 111.1.1... 31: [ . 1 2 2 1 ] 4 ((()())()) 111.1..1.. 32: [ . 1 2 3 4 ] 4 ((((())))) 11111..... 33: [ . 1 2 3 3 ] 4 (((()()))) 1111.1.... 34: [ . 1 2 3 2 ] 4 (((())())) 1111..1... 35: [ . 1 2 3 1 ] 4 (((()))()) 1111...1.. 36: [ . 1 2 3 . ] 3 (((())))() 1111....1. 37: [ . 1 2 2 . ] 3 ((()()))() 111.1...1. 38: [ . 1 2 1 . ] 3 ((())())() 111..1..1. 39: [ . 1 2 . . ] 2 ((()))()() 111...1.1. 40: [ . 1 1 . . ] 2 (()())()() 11.1..1.1. 41: [ . 1 . . . ] 1 (())()()() 11..1.1.1. 42: [ . . . . . ] 1 ()()()()() 1.1.1.1.1. Generation (in backward order) is (again) loopless and, at 510M/sec the fastest I know (by a solid margin over the 410M/sec of Aaron Williams fastest (cool-lex) beast). Forward generation is at 408M/sec still very OK. I'll write things up for arxiv.