Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001103
Mapping
St001103: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 1
[1,1]
 => 2
[3]
 => 1
[2,1]
 => 3
[1,1,1]
 => 5
[4]
 => 1
[3,1]
 => 4
[2,2]
 => 6
[2,1,1]
 => 10
[1,1,1,1]
 => 17
[5]
 => 1
[4,1]
 => 5
[3,2]
 => 10
[3,1,1]
 => 17
[2,2,1]
 => 24
[2,1,1,1]
 => 41
[1,1,1,1,1]
 => 70
[6]
 => 1
[5,1]
 => 6
[4,2]
 => 15
[4,1,1]
 => 26
[3,3]
 => 20
[3,2,1]
 => 48
[3,1,1,1]
 => 83
[2,2,2]
 => 67
[2,2,1,1]
 => 116
[2,1,1,1,1]
 => 201
[1,1,1,1,1,1]
 => 349
[7]
 => 1
[6,1]
 => 7
[5,2]
 => 21
[5,1,1]
 => 37
[4,3]
 => 35
[4,2,1]
 => 85
[4,1,1,1]
 => 149
[3,3,1]
 => 110
[3,2,2]
 => 153
[3,2,1,1]
 => 268
[3,1,1,1,1]
 => 470
[2,2,2,1]
 => 373
[2,2,1,1,1]
 => 654
[2,1,1,1,1,1]
 => 1148
[1,1,1,1,1,1,1]
 => 2017
[8]
 => 1
[7,1]
 => 8
[6,2]
 => 28
[6,1,1]
 => 50
[5,3]
 => 56
[5,2,1]
 => 138
Description
The number of words with multiplicities of the letters given by the partition, avoiding the consecutive pattern 123. The total number of words with letter multiplicities given by an integer partition is [[St000048]]. For example, there are twelve words with letters $0,0,1,2$ corresponding to the partition $[2,1,1]$. Two of these contain an increasing factor of length three: $0012$ and $0120$. Note that prescribing the multiplicities for different letters yields the same number. For example, there are also two words with letters $0,1,1,2$ containing an increasing factor of length three: $1012$ and $0121$. The number of words of length $n$ with letters in an alphabet of size $k$ avoiding the consecutive pattern $123$ is determined in [1].