ValleyComposition from StandardTableau

The composition cut at the valleys: entries i that are ascents after a descent.

StandardTableau → IntegerComposition

FindStat's Mp00295.

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

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Explore

Each element of StandardTableau at a size, and its image, applied in your browser; sizes past 6 are not offered.

Size

Properties

Sizes 1 to

Transport a statistic

Pick a statistic on IntegerComposition. Its distribution over the images of StandardTableau at each size is computed, and compared with the 25 statistics on StandardTableau: those that share it are the ones the map sends it to, as far as the sizes computed show.

Statistic Sizes 1 to

FindStat Mp00295

valley composition

Matched by value: our map agrees with FindStat's image on each of the 119 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

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

The composition corresponding to the valley set of a standard tableau.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00295 has the rest.