PeakComposition from StandardTableau
The composition cut at the peaks: entries i that are descents after an ascent.
FindStat's Mp00294. An entry is a descent when the next one sits in a lower row.
Called as CombinatorialMap(x, "PeakComposition"). The head's page has its examples.
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Each element of StandardTableau at a size, and its image, applied in your browser; sizes past 6 are not offered.
Properties
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.
FindStat Mp00294
peak 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.
| 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/Mp00294 has the rest.