OFFSET
1,1
COMMENTS
Also compositions matching the pattern (1,2).
A composition of n is a finite sequence of positive integers summing to n. The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.
LINKS
Keiichi Shigechi, Noncommutative crossing partitions, arXiv:2211.10958 [math.CO], 2022.
Wikipedia, Permutation pattern
EXAMPLE
The sequence of terms together with the corresponding compositions begins:
6: (1,2)
12: (1,3)
13: (1,2,1)
14: (1,1,2)
20: (2,3)
22: (2,1,2)
24: (1,4)
25: (1,3,1)
26: (1,2,2)
27: (1,2,1,1)
28: (1,1,3)
29: (1,1,2,1)
30: (1,1,1,2)
38: (3,1,2)
40: (2,4)
MATHEMATICA
stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]];
Select[Range[0, 100], MatchQ[stc[#], {___, x_, ___, y_, ___}/; x<y]&]
CROSSREFS
The complement A114994 is the avoiding version.
The (2,1)-matching version is A335486.
Patterns matching this pattern are counted by A002051 (by length).
Permutations of prime indices matching this pattern are counted by A335447.
These compositions are counted by A056823 (by sum).
Combinatory separations are counted by A269134.
Patterns matched by standard compositions are counted by A335454.
Minimal patterns avoided by a standard composition are counted by A335465.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 18 2020
STATUS
approved