GrayPrevious from BinaryWord
The previous word in the Gray code: flip the first letter when the ones are odd in number, else the letter after the first one.
FindStat's Mp00273, the inverse of GrayNext. The zero word gets its last letter flipped.
Called as CombinatorialMap(x, "GrayPrevious"). The head's page has its examples.
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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 BinaryWord. 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 Mp00273
Gray previous
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).
Bijectionas FindStat records them, checked by FindStat's contributors.
| Object | Image |
|---|---|
0 | 1 |
1 | 0 |
00 | 01 |
01 | 11 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00273 has the rest.