edit this statistic or download as text // json
Identifier
Values
=>
[1]=>1 [1,1]=>1 [2]=>1 [1,1,1]=>1 [1,2]=>1 [2,1]=>1 [3]=>1 [1,1,1,1]=>1 [1,1,2]=>1 [1,2,1]=>1 [1,3]=>2 [2,1,1]=>1 [2,2]=>2 [3,1]=>1 [4]=>1 [1,1,1,1,1]=>1 [1,1,1,2]=>1 [1,1,2,1]=>1 [1,1,3]=>3 [1,2,1,1]=>1 [1,2,2]=>2 [1,3,1]=>2 [1,4]=>3 [2,1,1,1]=>1 [2,1,2]=>1 [2,2,1]=>2 [2,3]=>2 [3,1,1]=>1 [3,2]=>3 [4,1]=>1 [5]=>1 [1,1,1,1,1,1]=>1 [1,1,1,1,2]=>1 [1,1,1,2,1]=>1 [1,1,1,3]=>4 [1,1,2,1,1]=>1 [1,1,2,2]=>2 [1,1,3,1]=>3 [1,1,4]=>6 [1,2,1,1,1]=>1 [1,2,1,2]=>1 [1,2,2,1]=>2 [1,2,3]=>2 [1,3,1,1]=>2 [1,3,2]=>5 [1,4,1]=>3 [1,5]=>4 [2,1,1,1,1]=>1 [2,1,1,2]=>1 [2,1,2,1]=>1 [2,1,3]=>3 [2,2,1,1]=>2 [2,2,2]=>5 [2,3,1]=>2 [2,4]=>5 [3,1,1,1]=>1 [3,1,2]=>1 [3,2,1]=>3 [3,3]=>5 [4,1,1]=>1 [4,2]=>4 [5,1]=>1 [6]=>1 [1,1,1,1,1,1,1]=>1 [1,1,1,1,1,2]=>1 [1,1,1,1,2,1]=>1 [1,1,1,1,3]=>5 [1,1,1,2,1,1]=>1 [1,1,1,2,2]=>2 [1,1,1,3,1]=>4 [1,1,1,4]=>10 [1,1,2,1,1,1]=>1 [1,1,2,1,2]=>1 [1,1,2,2,1]=>2 [1,1,2,3]=>2 [1,1,3,1,1]=>3 [1,1,3,2]=>7 [1,1,4,1]=>6 [1,1,5]=>10 [1,2,1,1,1,1]=>1 [1,2,1,1,2]=>1 [1,2,1,2,1]=>1 [1,2,1,3]=>3 [1,2,2,1,1]=>2 [1,2,2,2]=>5 [1,2,3,1]=>2 [1,2,4]=>7 [1,3,1,1,1]=>2 [1,3,1,2]=>2 [1,3,2,1]=>5 [1,3,3]=>12 [1,4,1,1]=>3 [1,4,2]=>9 [1,5,1]=>4 [1,6]=>5 [2,1,1,1,1,1]=>1 [2,1,1,1,2]=>1 [2,1,1,2,1]=>1 [2,1,1,3]=>4 [2,1,2,1,1]=>1 [2,1,2,2]=>2 [2,1,3,1]=>3 [2,1,4]=>9 [2,2,1,1,1]=>2 [2,2,1,2]=>2 [2,2,2,1]=>5 [2,2,3]=>5 [2,3,1,1]=>2 [2,3,2]=>7 [2,4,1]=>5 [2,5]=>9 [3,1,1,1,1]=>1 [3,1,1,2]=>1 [3,1,2,1]=>1 [3,1,3]=>4 [3,2,1,1]=>3 [3,2,2]=>9 [3,3,1]=>5 [3,4]=>5 [4,1,1,1]=>1 [4,1,2]=>1 [4,2,1]=>4 [4,3]=>9 [5,1,1]=>1 [5,2]=>5 [6,1]=>1 [7]=>1 [1,1,1,1,1,1,1,1]=>1 [1,1,1,1,1,1,2]=>1 [1,1,1,1,1,2,1]=>1 [1,1,1,1,1,3]=>6 [1,1,1,1,2,1,1]=>1 [1,1,1,1,2,2]=>2 [1,1,1,1,3,1]=>5 [1,1,1,1,4]=>15 [1,1,1,2,1,1,1]=>1 [1,1,1,2,1,2]=>1 [1,1,1,2,2,1]=>2 [1,1,1,2,3]=>2 [1,1,1,3,1,1]=>4 [1,1,1,3,2]=>9 [1,1,1,4,1]=>10 [1,1,1,5]=>20 [1,1,2,1,1,1,1]=>1 [1,1,2,1,1,2]=>1 [1,1,2,1,2,1]=>1 [1,1,2,1,3]=>3 [1,1,2,2,1,1]=>2 [1,1,2,2,2]=>5 [1,1,2,3,1]=>2 [1,1,2,4]=>9 [1,1,3,1,1,1]=>3 [1,1,3,1,2]=>3 [1,1,3,2,1]=>7 [1,1,3,3]=>21 [1,1,4,1,1]=>6 [1,1,4,2]=>16 [1,1,5,1]=>10 [1,1,6]=>15 [1,2,1,1,1,1,1]=>1 [1,2,1,1,1,2]=>1 [1,2,1,1,2,1]=>1 [1,2,1,1,3]=>4 [1,2,1,2,1,1]=>1 [1,2,1,2,2]=>2 [1,2,1,3,1]=>3 [1,2,1,4]=>12 [1,2,2,1,1,1]=>2 [1,2,2,1,2]=>2 [1,2,2,2,1]=>5 [1,2,2,3]=>5 [1,2,3,1,1]=>2 [1,2,3,2]=>7 [1,2,4,1]=>7 [1,2,5]=>16 [1,3,1,1,1,1]=>2 [1,3,1,1,2]=>2 [1,3,1,2,1]=>2 [1,3,1,3]=>9 [1,3,2,1,1]=>5 [1,3,2,2]=>14 [1,3,3,1]=>12 [1,3,4]=>12 [1,4,1,1,1]=>3 [1,4,1,2]=>3 [1,4,2,1]=>9 [1,4,3]=>30 [1,5,1,1]=>4 [1,5,2]=>14 [1,6,1]=>5 [1,7]=>6 [2,1,1,1,1,1,1]=>1 [2,1,1,1,1,2]=>1 [2,1,1,1,2,1]=>1 [2,1,1,1,3]=>5 [2,1,1,2,1,1]=>1 [2,1,1,2,2]=>2 [2,1,1,3,1]=>4 [2,1,1,4]=>14 [2,1,2,1,1,1]=>1 [2,1,2,1,2]=>1 [2,1,2,2,1]=>2 [2,1,2,3]=>2 [2,1,3,1,1]=>3 [2,1,3,2]=>7 [2,1,4,1]=>9 [2,1,5]=>19 [2,2,1,1,1,1]=>2 [2,2,1,1,2]=>2 [2,2,1,2,1]=>2 [2,2,1,3]=>7 [2,2,2,1,1]=>5 [2,2,2,2]=>14 [2,2,3,1]=>5 [2,2,4]=>21 [2,3,1,1,1]=>2 [2,3,1,2]=>2 [2,3,2,1]=>7 [2,3,3]=>12 [2,4,1,1]=>5 [2,4,2]=>21 [2,5,1]=>9 [2,6]=>14 [3,1,1,1,1,1]=>1 [3,1,1,1,2]=>1 [3,1,1,2,1]=>1 [3,1,1,3]=>5 [3,1,2,1,1]=>1 [3,1,2,2]=>2 [3,1,3,1]=>4 [3,1,4]=>9 [3,2,1,1,1]=>3 [3,2,1,2]=>3 [3,2,2,1]=>9 [3,2,3]=>9 [3,3,1,1]=>5 [3,3,2]=>21 [3,4,1]=>5 [3,5]=>14 [4,1,1,1,1]=>1 [4,1,1,2]=>1 [4,1,2,1]=>1 [4,1,3]=>5 [4,2,1,1]=>4 [4,2,2]=>14 [4,3,1]=>9 [4,4]=>14 [5,1,1,1]=>1 [5,1,2]=>1 [5,2,1]=>5 [5,3]=>14 [6,1,1]=>1 [6,2]=>6 [7,1]=>1 [8]=>1 [1,1,1,1,1,1,1,1,1]=>1 [1,1,1,1,1,1,1,2]=>1 [1,1,1,1,1,1,2,1]=>1 [1,1,1,1,1,1,3]=>7 [1,1,1,1,1,2,1,1]=>1 [1,1,1,1,1,2,2]=>2 [1,1,1,1,1,3,1]=>6 [1,1,1,1,1,4]=>21 [1,1,1,1,2,1,1,1]=>1 [1,1,1,1,2,1,2]=>1 [1,1,1,1,2,2,1]=>2 [1,1,1,1,2,3]=>2 [1,1,1,1,3,1,1]=>5 [1,1,1,1,3,2]=>11 [1,1,1,1,4,1]=>15 [1,1,1,1,5]=>35 [1,1,1,2,1,1,1,1]=>1 [1,1,1,2,1,1,2]=>1 [1,1,1,2,1,2,1]=>1 [1,1,1,2,1,3]=>3 [1,1,1,2,2,1,1]=>2 [1,1,1,2,2,2]=>5 [1,1,1,2,3,1]=>2 [1,1,1,2,4]=>11 [1,1,1,3,1,1,1]=>4 [1,1,1,3,1,2]=>4 [1,1,1,3,2,1]=>9 [1,1,1,3,3]=>32 [1,1,1,4,1,1]=>10 [1,1,1,4,2]=>25 [1,1,1,5,1]=>20 [1,1,1,6]=>35 [1,1,2,1,1,1,1,1]=>1 [1,1,2,1,1,1,2]=>1 [1,1,2,1,1,2,1]=>1 [1,1,2,1,1,3]=>4 [1,1,2,1,2,1,1]=>1 [1,1,2,1,2,2]=>2 [1,1,2,1,3,1]=>3 [1,1,2,1,4]=>15 [1,1,2,2,1,1,1]=>2 [1,1,2,2,1,2]=>2 [1,1,2,2,2,1]=>5 [1,1,2,2,3]=>5 [1,1,2,3,1,1]=>2 [1,1,2,3,2]=>7 [1,1,2,4,1]=>9 [1,1,2,5]=>25 [1,1,3,1,1,1,1]=>3 [1,1,3,1,1,2]=>3 [1,1,3,1,2,1]=>3 [1,1,3,1,3]=>15 [1,1,3,2,1,1]=>7 [1,1,3,2,2]=>19 [1,1,3,3,1]=>21 [1,1,3,4]=>21 [1,1,4,1,1,1]=>6 [1,1,4,1,2]=>6 [1,1,4,2,1]=>16 [1,1,4,3]=>67 [1,1,5,1,1]=>10 [1,1,5,2]=>30 [1,1,6,1]=>15 [1,1,7]=>21 [1,2,1,1,1,1,1,1]=>1 [1,2,1,1,1,1,2]=>1 [1,2,1,1,1,2,1]=>1 [1,2,1,1,1,3]=>5 [1,2,1,1,2,1,1]=>1 [1,2,1,1,2,2]=>2 [1,2,1,1,3,1]=>4 [1,2,1,1,4]=>18 [1,2,1,2,1,1,1]=>1 [1,2,1,2,1,2]=>1 [1,2,1,2,2,1]=>2 [1,2,1,2,3]=>2 [1,2,1,3,1,1]=>3 [1,2,1,3,2]=>7 [1,2,1,4,1]=>12 [1,2,1,5]=>31 [1,2,2,1,1,1,1]=>2 [1,2,2,1,1,2]=>2 [1,2,2,1,2,1]=>2 [1,2,2,1,3]=>7 [1,2,2,2,1,1]=>5 [1,2,2,2,2]=>14 [1,2,2,3,1]=>5 [1,2,2,4]=>26 [1,2,3,1,1,1]=>2 [1,2,3,1,2]=>2 [1,2,3,2,1]=>7 [1,2,3,3]=>12 [1,2,4,1,1]=>7 [1,2,4,2]=>28 [1,2,5,1]=>16 [1,2,6]=>30 [1,3,1,1,1,1,1]=>2 [1,3,1,1,1,2]=>2 [1,3,1,1,2,1]=>2 [1,3,1,1,3]=>11 [1,3,1,2,1,1]=>2 [1,3,1,2,2]=>4 [1,3,1,3,1]=>9 [1,3,1,4]=>21 [1,3,2,1,1,1]=>5 [1,3,2,1,2]=>5 [1,3,2,2,1]=>14 [1,3,2,3]=>14 [1,3,3,1,1]=>12 [1,3,3,2]=>42 [1,3,4,1]=>12 [1,3,5]=>42 [1,4,1,1,1,1]=>3 [1,4,1,1,2]=>3 [1,4,1,2,1]=>3 [1,4,1,3]=>17 [1,4,2,1,1]=>9 [1,4,2,2]=>28 [1,4,3,1]=>30 [1,4,4]=>56 [1,5,1,1,1]=>4 [1,5,1,2]=>4 [1,5,2,1]=>14 [1,5,3]=>58 [1,6,1,1]=>5 [1,6,2]=>20 [1,7,1]=>6 [1,8]=>7 [2,1,1,1,1,1,1,1]=>1 [2,1,1,1,1,1,2]=>1 [2,1,1,1,1,2,1]=>1 [2,1,1,1,1,3]=>6 [2,1,1,1,2,1,1]=>1 [2,1,1,1,2,2]=>2 [2,1,1,1,3,1]=>5 [2,1,1,1,4]=>20 [2,1,1,2,1,1,1]=>1 [2,1,1,2,1,2]=>1 [2,1,1,2,2,1]=>2 [2,1,1,2,3]=>2 [2,1,1,3,1,1]=>4 [2,1,1,3,2]=>9 [2,1,1,4,1]=>14 [2,1,1,5]=>34 [2,1,2,1,1,1,1]=>1 [2,1,2,1,1,2]=>1 [2,1,2,1,2,1]=>1 [2,1,2,1,3]=>3 [2,1,2,2,1,1]=>2 [2,1,2,2,2]=>5 [2,1,2,3,1]=>2 [2,1,2,4]=>11 [2,1,3,1,1,1]=>3 [2,1,3,1,2]=>3 [2,1,3,2,1]=>7 [2,1,3,3]=>21 [2,1,4,1,1]=>9 [2,1,4,2]=>23 [2,1,5,1]=>19 [2,1,6]=>34 [2,2,1,1,1,1,1]=>2 [2,2,1,1,1,2]=>2 [2,2,1,1,2,1]=>2 [2,2,1,1,3]=>9 [2,2,1,2,1,1]=>2 [2,2,1,2,2]=>4 [2,2,1,3,1]=>7 [2,2,1,4]=>33 [2,2,2,1,1,1]=>5 [2,2,2,1,2]=>5 [2,2,2,2,1]=>14 [2,2,2,3]=>14 [2,2,3,1,1]=>5 [2,2,3,2]=>19 [2,2,4,1]=>21 [2,2,5]=>56 [2,3,1,1,1,1]=>2 [2,3,1,1,2]=>2 [2,3,1,2,1]=>2 [2,3,1,3]=>9 [2,3,2,1,1]=>7 [2,3,2,2]=>23 [2,3,3,1]=>12 [2,3,4]=>12 [2,4,1,1,1]=>5 [2,4,1,2]=>5 [2,4,2,1]=>21 [2,4,3]=>42 [2,5,1,1]=>9 [2,5,2]=>44 [2,6,1]=>14 [2,7]=>20 [3,1,1,1,1,1,1]=>1 [3,1,1,1,1,2]=>1 [3,1,1,1,2,1]=>1 [3,1,1,1,3]=>6 [3,1,1,2,1,1]=>1 [3,1,1,2,2]=>2 [3,1,1,3,1]=>5 [3,1,1,4]=>14 [3,1,2,1,1,1]=>1 [3,1,2,1,2]=>1 [3,1,2,2,1]=>2 [3,1,2,3]=>2 [3,1,3,1,1]=>4 [3,1,3,2]=>9 [3,1,4,1]=>9 [3,1,5]=>28 [3,2,1,1,1,1]=>3 [3,2,1,1,2]=>3 [3,2,1,2,1]=>3 [3,2,1,3]=>12 [3,2,2,1,1]=>9 [3,2,2,2]=>28 [3,2,3,1]=>9 [3,2,4]=>30 [3,3,1,1,1]=>5 [3,3,1,2]=>5 [3,3,2,1]=>21 [3,3,3]=>42 [3,4,1,1]=>5 [3,4,2]=>26 [3,5,1]=>14 [3,6]=>28 [4,1,1,1,1,1]=>1 [4,1,1,1,2]=>1 [4,1,1,2,1]=>1 [4,1,1,3]=>6 [4,1,2,1,1]=>1 [4,1,2,2]=>2 [4,1,3,1]=>5 [4,1,4]=>14 [4,2,1,1,1]=>4 [4,2,1,2]=>4 [4,2,2,1]=>14 [4,2,3]=>14 [4,3,1,1]=>9 [4,3,2]=>44 [4,4,1]=>14 [4,5]=>14 [5,1,1,1,1]=>1 [5,1,1,2]=>1 [5,1,2,1]=>1 [5,1,3]=>6 [5,2,1,1]=>5 [5,2,2]=>20 [5,3,1]=>14 [5,4]=>28 [6,1,1,1]=>1 [6,1,2]=>1 [6,2,1]=>6 [6,3]=>20 [7,1,1]=>1 [7,2]=>7 [8,1]=>1 [9]=>1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The number of standard composition tableaux of the composition.
See [1, Def. 4.2.6].
Apparently, the total number of tableaux of given size is the number of involutions.
References
[1] Luoto, K., Mykytiuk, S., van Willigenburg, S. An introduction to quasisymmetric Schur functions MathSciNet:3097867
Code
def statistic(c):
    F = QuasiSymmetricFunctions(ZZ).F()
    QS = QuasiSymmetricFunctions(ZZ).QS()
    return sum(coeff for _, coeff in F(QS(c)))
Created
May 19, 2017 at 23:08 by Martin Rubey
Updated
Nov 19, 2017 at 22:03 by Christian Stump