DescentWordPreimageCount on BinaryWord
The permutations whose descent word is this word.
FindStat's St000529, the size of the preimage of the descent word map. The word has length N - 1; the count is by inclusion-exclusion over the descents.
Called as CombinatorialStat(x, "DescentWordPreimageCount"). 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 St000529
The number of permutations whose descent word is the given binary word.
| Object | Value |
|---|---|
0 | 1 |
1 | 1 |
00 | 1 |
01 | 2 |
10 | 2 |
11 | 1 |
000 | 1 |
001 | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000529 has the rest.