ReducedWordSupport on Permutation
The simple reflections in a reduced word: the i < n with some entry of p(1), ..., p(i) larger than i.
The size of the support in the Coxeter sense: the i for which p does not preserve {1, ..., i}. PermutationSupport counts the moved points instead.
Called as CombinatorialStat(x, "ReducedWordSupport"). The head's page has its examples.
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Distribution
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FindStat St000019
The cardinality of the support of a permutation.
| Object | Value |
|---|---|
[1] | 0 |
[1,2] | 0 |
[2,1] | 1 |
[1,2,3] | 0 |
[1,3,2] | 1 |
[2,1,3] | 1 |
[2,3,1] | 2 |
[3,1,2] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000019 has the rest.