BalancedPrefixCount on BinaryWord
The nonempty prefixes with as many 0s as 1s.
The returns of the word, read as a lattice path, to the main diagonal.
Called as CombinatorialStat(x, "BalancedPrefixCount"). 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 St001355
Number of non-empty prefixes of a binary word that contain equally many 0's and 1's.
| Object | Value |
|---|---|
0 | 0 |
1 | 0 |
00 | 0 |
01 | 1 |
10 | 1 |
11 | 0 |
000 | 0 |
001 | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001355 has the rest.