TouchComposition from DyckPath

The semilengths of the primitive pieces between a path's returns to the diagonal.

DyckPath → IntegerCompositionsurjection

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

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Each element of DyckPath 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 IntegerComposition. Its distribution over the images of DyckPath at each size is computed, and compared with the 171 statistics on DyckPath: those that share it are the ones the map sends it to, as far as the sizes computed show.

Statistic Sizes 1 to

FindStat Mp00100

touch composition

Matched by value: our map agrees with FindStat's image on each of the 196 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.

Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00100 has the rest.