Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000620
Mapping
St000620: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2]
 => 0
[1,1]
 => 1
[3]
 => 1
[2,1]
 => 1
[1,1,1]
 => 1
[4]
 => 0
[3,1]
 => 2
[2,2]
 => 1
[2,1,1]
 => 2
[1,1,1,1]
 => 1
[5]
 => 1
[4,1]
 => 2
[3,2]
 => 3
[3,1,1]
 => 4
[2,2,1]
 => 3
[2,1,1,1]
 => 3
[1,1,1,1,1]
 => 1
[6]
 => 0
[5,1]
 => 3
[4,2]
 => 5
[4,1,1]
 => 6
[3,3]
 => 3
[3,2,1]
 => 10
[3,1,1,1]
 => 7
[2,2,2]
 => 3
[2,2,1,1]
 => 6
[2,1,1,1,1]
 => 4
[1,1,1,1,1,1]
 => 1
[7]
 => 1
[6,1]
 => 3
[5,2]
 => 8
[5,1,1]
 => 9
[4,3]
 => 8
[4,2,1]
 => 21
[4,1,1,1]
 => 13
[3,3,1]
 => 13
[3,2,2]
 => 13
[3,2,1,1]
 => 23
[3,1,1,1,1]
 => 11
[2,2,2,1]
 => 9
[2,2,1,1,1]
 => 10
[2,1,1,1,1,1]
 => 5
[1,1,1,1,1,1,1]
 => 1
[8]
 => 0
[7,1]
 => 4
[6,2]
 => 11
[6,1,1]
 => 12
[5,3]
 => 16
[5,2,1]
 => 38
[5,1,1,1]
 => 22
Description
The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is odd. The case of an even minimum is [[St000621]].