ConnectivityWord from Permutation

Letter i is 1 when the first i entries are all smaller than the rest: the connectivity set as a binary word.

FindStat's Mp00114. One letter shorter than the permutation; the word is all 0 exactly when the permutation is connected.

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

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Each element of Permutation at a size, and its image, applied in your browser; sizes past 7 are not offered.

Size

Properties

Sizes 1 to

Transport a statistic

Pick a statistic on BinaryWord. Its distribution over the images of Permutation at each size is computed, and compared with the 323 statistics on Permutation: those that share it are the ones the map sends it to, as far as the sizes computed show.

Statistic Sizes 1 to

FindStat Mp00114

connectivity set

Matched by value: our map agrees with FindStat's image on each of the 873 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

SurjectionGraded mapas FindStat records them, checked by FindStat's contributors.

The connectivity set of a permutation as a binary word.

Object	Image
`[1]`
`[1,2]`	`1`
`[2,1]`	`0`
`[1,2,3]`	`11`

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00114 has the rest.