ShortestDistinctWindowLength on Permutation

The least k such that no two windows of k consecutive entries are order isomorphic.

On Permutation

The whole word is one window, so the least exists.

Called as CombinatorialStat(x, "ShortestDistinctWindowLength"). The head's page has its examples.

Live

Distribution

Over SymmetricGroup at each size, tallied here in your browser; sizes past 8 are not offered.

Sizes 1 to

FindStat St000923

The minimal number with no two order isomorphic substrings of this length in a permutation.

Object	Value
[1,2]	2
[2,1]	2
[1,2,3]	3
[1,3,2]	2
[2,1,3]	2
[2,3,1]	2
[3,1,2]	2
[3,2,1]	3

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000923 has the rest.