DistinctSubsequenceCount on BinaryWord
The distinct subsequences, the empty one included.
FindStat's St000518. With d(j) the count for the first j letters, d(j) = 2 d(j - 1) less d(p - 1), where p is the latest earlier position holding the same letter, if any.
Called as CombinatorialStat(x, "DistinctSubsequenceCount"). The head's page has its examples.
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Distribution
Over BinaryWords at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000518
The number of distinct subsequences in a binary word.
| Object | Value |
|---|---|
0 | 2 |
1 | 2 |
00 | 3 |
01 | 4 |
10 | 4 |
11 | 3 |
000 | 4 |
001 | 6 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000518 has the rest.