OccurrencesOfUDU on DyckPath
Occurrences of an up, a down and an up step.
Called as CombinatorialStat(x, "OccurrencesOfUDU"). The head's page has its examples.
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Distribution
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FindStat St000932
The number of occurrences of the pattern UDU in a Dyck path.
| Object | Value |
|---|---|
[1,0,1,0] | 1 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 2 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 1 |
[1,1,1,0,0,0] | 0 |
[1,0,1,0,1,0,1,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000932 has the rest.
FindStat St001067
The number of simple modules of dominant dimension at least two in the linear Nakayama algebra corresponding to a Dyck path.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 2 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 1 |
[1,1,1,0,0,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001067 has the rest.
FindStat St001223
Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 2 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 1 |
[1,1,1,0,0,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001223 has the rest.