Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001097
Mapping
St001097: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2]
 => 0
[1,1]
 => 2
[3]
 => 0
[2,1]
 => 1
[1,1,1]
 => 6
[4]
 => 0
[3,1]
 => 0
[2,2]
 => 2
[2,1,1]
 => 6
[1,1,1,1]
 => 24
[5]
 => 0
[4,1]
 => 0
[3,2]
 => 1
[3,1,1]
 => 2
[2,2,1]
 => 12
[2,1,1,1]
 => 36
[1,1,1,1,1]
 => 120
[6]
 => 0
[5,1]
 => 0
[4,2]
 => 0
[4,1,1]
 => 0
[3,3]
 => 2
[3,2,1]
 => 10
[3,1,1,1]
 => 24
[2,2,2]
 => 30
[2,2,1,1]
 => 84
[2,1,1,1,1]
 => 240
[1,1,1,1,1,1]
 => 720
[7]
 => 0
[6,1]
 => 0
[5,2]
 => 0
[5,1,1]
 => 0
[4,3]
 => 1
[4,2,1]
 => 3
[4,1,1,1]
 => 6
[3,3,1]
 => 18
[3,2,2]
 => 38
[3,2,1,1]
 => 96
[3,1,1,1,1]
 => 240
[2,2,2,1]
 => 246
[2,2,1,1,1]
 => 660
[2,1,1,1,1,1]
 => 1800
[1,1,1,1,1,1,1]
 => 5040
[8]
 => 0
[7,1]
 => 0
[6,2]
 => 0
[6,1,1]
 => 0
[5,3]
 => 0
[5,2,1]
 => 0
[5,1,1,1]
 => 0
Description
The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. For a generating function $f$ the associated formal group law is the symmetric function $f(f^{(-1)}(x_1) + f^{(-1)}(x_2), \dots)$, see [1]. This statistic records the coefficient of the monomial symmetric function $m_\lambda$ in the formal group law for linear orders, with generating function $f(x) = x/(1-x)$, see [1, sec. 3.4]. This statistic gives the number of Smirnov arrangements of a set of letters with $\lambda_i$ of the $i$th letter, where a Smirnov word is a word with no repeated adjacent letters. e.g., [3,2,1] = > 10 since there are 10 Smirnov rearrangements of the word 'aaabbc': 'ababac', 'ababca', 'abacab', 'abacba', 'abcaba', 'acabab', 'acbaba', 'babaca', 'bacaba', 'cababa'.