Identifier
Values
=>
Cc0002;cc-rep
[2]=>2
[1,1]=>1
[3]=>3
[2,1]=>4
[1,1,1]=>1
[4]=>4
[3,1]=>5
[2,2]=>2
[2,1,1]=>5
[1,1,1,1]=>1
[5]=>5
[4,1]=>6
[3,2]=>6
[3,1,1]=>6
[2,2,1]=>4
[2,1,1,1]=>6
[1,1,1,1,1]=>1
[6]=>6
[5,1]=>7
[4,2]=>7
[4,1,1]=>7
[3,3]=>3
[3,2,1]=>9
[3,1,1,1]=>7
[2,2,2]=>2
[2,2,1,1]=>5
[2,1,1,1,1]=>7
[1,1,1,1,1,1]=>1
[7]=>7
[6,1]=>8
[5,2]=>8
[5,1,1]=>8
[4,3]=>8
[4,2,1]=>10
[4,1,1,1]=>8
[3,3,1]=>5
[3,2,2]=>7
[3,2,1,1]=>11
[3,1,1,1,1]=>8
[2,2,2,1]=>4
[2,2,1,1,1]=>6
[2,1,1,1,1,1]=>8
[1,1,1,1,1,1,1]=>1
[8]=>8
[7,1]=>9
[6,2]=>9
[6,1,1]=>9
[5,3]=>9
[5,2,1]=>11
[5,1,1,1]=>9
[4,4]=>4
[4,3,1]=>11
[4,2,2]=>8
[4,2,1,1]=>12
[4,1,1,1,1]=>9
[3,3,2]=>6
[3,3,1,1]=>6
[3,2,2,1]=>10
[3,2,1,1,1]=>13
[3,1,1,1,1,1]=>9
[2,2,2,2]=>2
[2,2,2,1,1]=>5
[2,2,1,1,1,1]=>7
[2,1,1,1,1,1,1]=>9
[1,1,1,1,1,1,1,1]=>1
[9]=>9
[8,1]=>10
[7,2]=>10
[7,1,1]=>10
[6,3]=>10
[6,2,1]=>12
[6,1,1,1]=>10
[5,4]=>10
[5,3,1]=>12
[5,2,2]=>9
[5,2,1,1]=>13
[5,1,1,1,1]=>10
[4,4,1]=>6
[4,3,2]=>12
[4,3,1,1]=>13
[4,2,2,1]=>11
[4,2,1,1,1]=>14
[4,1,1,1,1,1]=>10
[3,3,3]=>3
[3,3,2,1]=>9
[3,3,1,1,1]=>7
[3,2,2,2]=>8
[3,2,2,1,1]=>12
[3,2,1,1,1,1]=>15
[3,1,1,1,1,1,1]=>10
[2,2,2,2,1]=>4
[2,2,2,1,1,1]=>6
[2,2,1,1,1,1,1]=>8
[2,1,1,1,1,1,1,1]=>10
[1,1,1,1,1,1,1,1,1]=>1
[10]=>10
[9,1]=>11
[8,2]=>11
[8,1,1]=>11
[7,3]=>11
[7,2,1]=>13
[7,1,1,1]=>11
[6,4]=>11
[6,3,1]=>13
[6,2,2]=>10
[6,2,1,1]=>14
[6,1,1,1,1]=>11
[5,5]=>5
[5,4,1]=>13
[5,3,2]=>13
[5,3,1,1]=>14
[5,2,2,1]=>12
[5,2,1,1,1]=>15
[5,1,1,1,1,1]=>11
[4,4,2]=>7
[4,4,1,1]=>7
[4,3,3]=>9
[4,3,2,1]=>16
[4,3,1,1,1]=>15
[4,2,2,2]=>9
[4,2,2,1,1]=>13
[4,2,1,1,1,1]=>16
[4,1,1,1,1,1,1]=>11
[3,3,3,1]=>5
[3,3,2,2]=>7
[3,3,2,1,1]=>11
[3,3,1,1,1,1]=>8
[3,2,2,2,1]=>11
[3,2,2,1,1,1]=>14
[3,2,1,1,1,1,1]=>17
[3,1,1,1,1,1,1,1]=>11
[2,2,2,2,2]=>2
[2,2,2,2,1,1]=>5
[2,2,2,1,1,1,1]=>7
[2,2,1,1,1,1,1,1]=>9
[2,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,1,1,1,1,1,1]=>1
[11]=>11
[10,1]=>12
[9,2]=>12
[9,1,1]=>12
[8,3]=>12
[8,2,1]=>14
[8,1,1,1]=>12
[7,4]=>12
[7,3,1]=>14
[7,2,2]=>11
[7,2,1,1]=>15
[7,1,1,1,1]=>12
[6,5]=>12
[6,4,1]=>14
[6,3,2]=>14
[6,3,1,1]=>15
[6,2,2,1]=>13
[6,2,1,1,1]=>16
[6,1,1,1,1,1]=>12
[5,5,1]=>7
[5,4,2]=>14
[5,4,1,1]=>15
[5,3,3]=>10
[5,3,2,1]=>17
[5,3,1,1,1]=>16
[5,2,2,2]=>10
[5,2,2,1,1]=>14
[5,2,1,1,1,1]=>17
[5,1,1,1,1,1,1]=>12
[4,4,3]=>8
[4,4,2,1]=>10
[4,4,1,1,1]=>8
[4,3,3,1]=>12
[4,3,2,2]=>14
[4,3,2,1,1]=>19
[4,3,1,1,1,1]=>17
[4,2,2,2,1]=>12
[4,2,2,1,1,1]=>15
[4,2,1,1,1,1,1]=>18
[4,1,1,1,1,1,1,1]=>12
[3,3,3,2]=>6
[3,3,3,1,1]=>6
[3,3,2,2,1]=>10
[3,3,2,1,1,1]=>13
[3,3,1,1,1,1,1]=>9
[3,2,2,2,2]=>9
[3,2,2,2,1,1]=>13
[3,2,2,1,1,1,1]=>16
[3,2,1,1,1,1,1,1]=>19
[3,1,1,1,1,1,1,1,1]=>12
[2,2,2,2,2,1]=>4
[2,2,2,2,1,1,1]=>6
[2,2,2,1,1,1,1,1]=>8
[2,2,1,1,1,1,1,1,1]=>10
[2,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,1,1,1,1,1,1,1]=>1
[12]=>12
[11,1]=>13
[10,2]=>13
[10,1,1]=>13
[9,3]=>13
[9,2,1]=>15
[9,1,1,1]=>13
[8,4]=>13
[8,3,1]=>15
[8,2,2]=>12
[8,2,1,1]=>16
[8,1,1,1,1]=>13
[7,5]=>13
[7,4,1]=>15
[7,3,2]=>15
[7,3,1,1]=>16
[7,2,2,1]=>14
[7,2,1,1,1]=>17
[7,1,1,1,1,1]=>13
[6,6]=>6
[6,5,1]=>15
[6,4,2]=>15
[6,4,1,1]=>16
[6,3,3]=>11
[6,3,2,1]=>18
[6,3,1,1,1]=>17
[6,2,2,2]=>11
[6,2,2,1,1]=>15
[6,2,1,1,1,1]=>18
[6,1,1,1,1,1,1]=>13
[5,5,2]=>8
[5,5,1,1]=>8
[5,4,3]=>15
[5,4,2,1]=>18
[5,4,1,1,1]=>17
[5,3,3,1]=>13
[5,3,2,2]=>15
[5,3,2,1,1]=>20
[5,3,1,1,1,1]=>18
[5,2,2,2,1]=>13
[5,2,2,1,1,1]=>16
[5,2,1,1,1,1,1]=>19
[5,1,1,1,1,1,1,1]=>13
[4,4,4]=>4
[4,4,3,1]=>11
[4,4,2,2]=>8
[4,4,2,1,1]=>12
[4,4,1,1,1,1]=>9
[4,3,3,2]=>13
[4,3,3,1,1]=>14
[4,3,2,2,1]=>18
[4,3,2,1,1,1]=>22
[4,3,1,1,1,1,1]=>19
[4,2,2,2,2]=>10
[4,2,2,2,1,1]=>14
[4,2,2,1,1,1,1]=>17
[4,2,1,1,1,1,1,1]=>20
[4,1,1,1,1,1,1,1,1]=>13
[3,3,3,3]=>3
[3,3,3,2,1]=>9
[3,3,3,1,1,1]=>7
[3,3,2,2,2]=>8
[3,3,2,2,1,1]=>12
[3,3,2,1,1,1,1]=>15
[3,3,1,1,1,1,1,1]=>10
[3,2,2,2,2,1]=>12
[3,2,2,2,1,1,1]=>15
[3,2,2,1,1,1,1,1]=>18
[3,2,1,1,1,1,1,1,1]=>21
[3,1,1,1,1,1,1,1,1,1]=>13
[2,2,2,2,2,2]=>2
[2,2,2,2,2,1,1]=>5
[2,2,2,2,1,1,1,1]=>7
[2,2,2,1,1,1,1,1,1]=>9
[2,2,1,1,1,1,1,1,1,1]=>11
[2,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,1,1,1,1,1,1,1,1]=>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
Description
The major index of an integer partition when read from bottom to top.
This is the sum of the positions of the corners of the shape of an integer partition when reading from bottom to top.
For example, the partition $\lambda = (8,6,6,4,3,3)$ has corners at positions 3,6,9, and 13, giving a major index of 31.
This is the sum of the positions of the corners of the shape of an integer partition when reading from bottom to top.
For example, the partition $\lambda = (8,6,6,4,3,3)$ has corners at positions 3,6,9, and 13, giving a major index of 31.
Code
def statistic(L):
L = list(L) + [0]
return sum( len(L)-i-2+L[i] for i in range(len(L)-1) if L[i] > L[i+1] )
Created
Apr 10, 2017 at 15:37 by Christian Stump
Updated
Apr 10, 2017 at 15:37 by Christian Stump
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!