edit this statistic or download as text // json
Identifier
Values
=>
Cc0002;cc-rep
[]=>1 [1]=>1 [2]=>2 [1,1]=>1 [3]=>3 [2,1]=>2 [1,1,1]=>1 [4]=>5 [3,1]=>4 [2,2]=>3 [2,1,1]=>2 [1,1,1,1]=>1 [5]=>7 [4,1]=>6 [3,2]=>5 [3,1,1]=>4 [2,2,1]=>3 [2,1,1,1]=>2 [1,1,1,1,1]=>1 [6]=>11 [5,1]=>10 [4,2]=>9 [4,1,1]=>7 [3,3]=>7 [3,2,1]=>6 [3,1,1,1]=>4 [2,2,2]=>4 [2,2,1,1]=>3 [2,1,1,1,1]=>2 [1,1,1,1,1,1]=>1 [7]=>15 [6,1]=>14 [5,2]=>13 [5,1,1]=>11 [4,3]=>11 [4,2,1]=>10 [4,1,1,1]=>7 [3,3,1]=>8 [3,2,2]=>7 [3,2,1,1]=>6 [3,1,1,1,1]=>4 [2,2,2,1]=>4 [2,2,1,1,1]=>3 [2,1,1,1,1,1]=>2 [1,1,1,1,1,1,1]=>1 [8]=>22 [7,1]=>21 [6,2]=>20 [6,1,1]=>17 [5,3]=>18 [5,2,1]=>16 [5,1,1,1]=>12 [4,4]=>15 [4,3,1]=>14 [4,2,2]=>13 [4,2,1,1]=>11 [4,1,1,1,1]=>7 [3,3,2]=>10 [3,3,1,1]=>9 [3,2,2,1]=>8 [3,2,1,1,1]=>6 [3,1,1,1,1,1]=>4 [2,2,2,2]=>5 [2,2,2,1,1]=>4 [2,2,1,1,1,1]=>3 [2,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1]=>1 [9]=>30 [8,1]=>29 [7,2]=>28 [7,1,1]=>25 [6,3]=>26 [6,2,1]=>24 [6,1,1,1]=>18 [5,4]=>23 [5,3,1]=>22 [5,2,2]=>20 [5,2,1,1]=>17 [5,1,1,1,1]=>12 [4,4,1]=>18 [4,3,2]=>17 [4,3,1,1]=>15 [4,2,2,1]=>14 [4,2,1,1,1]=>11 [4,1,1,1,1,1]=>7 [3,3,3]=>12 [3,3,2,1]=>11 [3,3,1,1,1]=>9 [3,2,2,2]=>9 [3,2,2,1,1]=>8 [3,2,1,1,1,1]=>6 [3,1,1,1,1,1,1]=>4 [2,2,2,2,1]=>5 [2,2,2,1,1,1]=>4 [2,2,1,1,1,1,1]=>3 [2,1,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1,1]=>1 [10]=>42 [9,1]=>41 [8,2]=>40 [8,1,1]=>36 [7,3]=>38 [7,2,1]=>35 [7,1,1,1]=>28 [6,4]=>35 [6,3,1]=>33 [6,2,2]=>31 [6,2,1,1]=>27 [6,1,1,1,1]=>19 [5,5]=>30 [5,4,1]=>29 [5,3,2]=>28 [5,3,1,1]=>25 [5,2,2,1]=>23 [5,2,1,1,1]=>18 [5,1,1,1,1,1]=>12 [4,4,2]=>23 [4,4,1,1]=>21 [4,3,3]=>21 [4,3,2,1]=>20 [4,3,1,1,1]=>16 [4,2,2,2]=>17 [4,2,2,1,1]=>15 [4,2,1,1,1,1]=>11 [4,1,1,1,1,1,1]=>7 [3,3,3,1]=>14 [3,3,2,2]=>13 [3,3,2,1,1]=>12 [3,3,1,1,1,1]=>9 [3,2,2,2,1]=>10 [3,2,2,1,1,1]=>8 [3,2,1,1,1,1,1]=>6 [3,1,1,1,1,1,1,1]=>4 [2,2,2,2,2]=>6 [2,2,2,2,1,1]=>5 [2,2,2,1,1,1,1]=>4 [2,2,1,1,1,1,1,1]=>3 [2,1,1,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1,1,1]=>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 integer partitions of n that are dominated by an integer partition.
A partition $\lambda = (\lambda_1,\ldots,\lambda_n) \vdash n$ dominates a partition $\mu = (\mu_1,\ldots,\mu_n) \vdash n$ if $\sum_{i=1}^k (\lambda_i - \mu_i) \geq 0$ for all $k$.
Code
def statistic(L):
    return len(L.dominated_partitions())
Created
Dec 08, 2015 at 16:23 by Christian Stump
Updated
Oct 29, 2017 at 20:53 by Martin Rubey