CodeComposition from BinaryWord
The composition whose code is the word with a 1 put in front: each 1 opens a part, of 1 plus the zeros after it.
FindStat's Mp00178, Sage's from_code. An injection one size up (the empty composition has no preimage); the inverse of CodeWord on the words that start with 1. Not IntegerComposition, whose word marks the cuts.
Called as CombinatorialMap(x, "CodeComposition"). The head's page has its examples.
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Explore
Each element of BinaryWord 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 BinaryWord at each size is computed, and compared with the 59 statistics on BinaryWord: those that share it are the ones the map sends it to, as far as the sizes computed show.
FindStat Mp00178
to composition
Matched by value: our map agrees with FindStat's image on each of the 126 rows of size at most 6 we can read (0 unread; its table has 1200 rows).
InjectionGraded mapas FindStat records them, checked by FindStat's contributors.
| Object | Image |
|---|---|
0 | [2] |
1 | [1,1] |
00 | [3] |
01 | [2,1] |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00178 has the rest.