Identifier
Values
=>
Cc0002;cc-rep
[]=>0
[1]=>1
[2]=>2
[1,1]=>1
[3]=>2
[2,1]=>3
[1,1,1]=>1
[4]=>2
[3,1]=>4
[2,2]=>3
[2,1,1]=>2
[1,1,1,1]=>1
[5]=>2
[4,1]=>3
[3,2]=>5
[3,1,1]=>4
[2,2,1]=>3
[2,1,1,1]=>2
[1,1,1,1,1]=>1
[6]=>2
[5,1]=>3
[4,2]=>5
[4,1,1]=>4
[3,3]=>4
[3,2,1]=>6
[3,1,1,1]=>3
[2,2,2]=>3
[2,2,1,1]=>2
[2,1,1,1,1]=>2
[1,1,1,1,1,1]=>1
[7]=>2
[6,1]=>3
[5,2]=>4
[5,1,1]=>3
[4,3]=>5
[4,2,1]=>7
[4,1,1,1]=>4
[3,3,1]=>6
[3,2,2]=>5
[3,2,1,1]=>4
[3,1,1,1,1]=>3
[2,2,2,1]=>3
[2,2,1,1,1]=>2
[2,1,1,1,1,1]=>2
[1,1,1,1,1,1,1]=>1
[8]=>2
[7,1]=>3
[6,2]=>4
[6,1,1]=>3
[5,3]=>5
[5,2,1]=>5
[5,1,1,1]=>4
[4,4]=>4
[4,3,1]=>8
[4,2,2]=>7
[4,2,1,1]=>6
[4,1,1,1,1]=>3
[3,3,2]=>6
[3,3,1,1]=>5
[3,2,2,1]=>4
[3,2,1,1,1]=>4
[3,1,1,1,1,1]=>3
[2,2,2,2]=>3
[2,2,2,1,1]=>2
[2,2,1,1,1,1]=>2
[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1]=>1
[9]=>2
[8,1]=>3
[7,2]=>4
[7,1,1]=>3
[6,3]=>4
[6,2,1]=>5
[6,1,1,1]=>3
[5,4]=>5
[5,3,1]=>7
[5,2,2]=>6
[5,2,1,1]=>5
[5,1,1,1,1]=>4
[4,4,1]=>6
[4,3,2]=>9
[4,3,1,1]=>8
[4,2,2,1]=>7
[4,2,1,1,1]=>5
[4,1,1,1,1,1]=>3
[3,3,3]=>5
[3,3,2,1]=>6
[3,3,1,1,1]=>4
[3,2,2,2]=>4
[3,2,2,1,1]=>3
[3,2,1,1,1,1]=>4
[3,1,1,1,1,1,1]=>3
[2,2,2,2,1]=>3
[2,2,2,1,1,1]=>2
[2,2,1,1,1,1,1]=>2
[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1]=>1
[10]=>2
[9,1]=>3
[8,2]=>4
[8,1,1]=>3
[7,3]=>4
[7,2,1]=>5
[7,1,1,1]=>3
[6,4]=>5
[6,3,1]=>6
[6,2,2]=>5
[6,2,1,1]=>4
[6,1,1,1,1]=>4
[5,5]=>4
[5,4,1]=>6
[5,3,2]=>9
[5,3,1,1]=>8
[5,2,2,1]=>7
[5,2,1,1,1]=>5
[5,1,1,1,1,1]=>3
[4,4,2]=>8
[4,4,1,1]=>7
[4,3,3]=>7
[4,3,2,1]=>10
[4,3,1,1,1]=>6
[4,2,2,2]=>6
[4,2,2,1,1]=>5
[4,2,1,1,1,1]=>5
[4,1,1,1,1,1,1]=>3
[3,3,3,1]=>6
[3,3,2,2]=>5
[3,3,2,1,1]=>4
[3,3,1,1,1,1]=>4
[3,2,2,2,1]=>4
[3,2,2,1,1,1]=>3
[3,2,1,1,1,1,1]=>4
[3,1,1,1,1,1,1,1]=>3
[2,2,2,2,2]=>3
[2,2,2,2,1,1]=>2
[2,2,2,1,1,1,1]=>2
[2,2,1,1,1,1,1,1]=>2
[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1]=>1
[11]=>2
[10,1]=>3
[9,2]=>4
[9,1,1]=>3
[8,3]=>4
[8,2,1]=>5
[8,1,1,1]=>3
[7,4]=>4
[7,3,1]=>6
[7,2,2]=>5
[7,2,1,1]=>4
[7,1,1,1,1]=>3
[6,5]=>5
[6,4,1]=>6
[6,3,2]=>7
[6,3,1,1]=>6
[6,2,2,1]=>5
[6,2,1,1,1]=>5
[6,1,1,1,1,1]=>4
[5,5,1]=>5
[5,4,2]=>9
[5,4,1,1]=>8
[5,3,3]=>8
[5,3,2,1]=>11
[5,3,1,1,1]=>7
[5,2,2,2]=>7
[5,2,2,1,1]=>6
[5,2,1,1,1,1]=>4
[5,1,1,1,1,1,1]=>3
[4,4,3]=>7
[4,4,2,1]=>10
[4,4,1,1,1]=>6
[4,3,3,1]=>9
[4,3,2,2]=>8
[4,3,2,1,1]=>7
[4,3,1,1,1,1]=>6
[4,2,2,2,1]=>5
[4,2,2,1,1,1]=>5
[4,2,1,1,1,1,1]=>5
[4,1,1,1,1,1,1,1]=>3
[3,3,3,2]=>6
[3,3,3,1,1]=>5
[3,3,2,2,1]=>4
[3,3,2,1,1,1]=>4
[3,3,1,1,1,1,1]=>4
[3,2,2,2,2]=>4
[3,2,2,2,1,1]=>3
[3,2,2,1,1,1,1]=>3
[3,2,1,1,1,1,1,1]=>4
[3,1,1,1,1,1,1,1,1]=>3
[2,2,2,2,2,1]=>3
[2,2,2,2,1,1,1]=>2
[2,2,2,1,1,1,1,1]=>2
[2,2,1,1,1,1,1,1,1]=>2
[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,1]=>1
[12]=>2
[11,1]=>3
[10,2]=>4
[10,1,1]=>3
[9,3]=>4
[9,2,1]=>5
[9,1,1,1]=>3
[8,4]=>4
[8,3,1]=>6
[8,2,2]=>5
[8,2,1,1]=>4
[8,1,1,1,1]=>3
[7,5]=>5
[7,4,1]=>5
[7,3,2]=>7
[7,3,1,1]=>6
[7,2,2,1]=>5
[7,2,1,1,1]=>4
[7,1,1,1,1,1]=>4
[6,6]=>4
[6,5,1]=>6
[6,4,2]=>8
[6,4,1,1]=>7
[6,3,3]=>7
[6,3,2,1]=>8
[6,3,1,1,1]=>6
[6,2,2,2]=>6
[6,2,2,1,1]=>5
[6,2,1,1,1,1]=>5
[6,1,1,1,1,1,1]=>3
[5,5,2]=>7
[5,5,1,1]=>6
[5,4,3]=>9
[5,4,2,1]=>12
[5,4,1,1,1]=>8
[5,3,3,1]=>11
[5,3,2,2]=>10
[5,3,2,1,1]=>9
[5,3,1,1,1,1]=>6
[5,2,2,2,1]=>7
[5,2,2,1,1,1]=>5
[5,2,1,1,1,1,1]=>4
[5,1,1,1,1,1,1,1]=>3
[4,4,4]=>6
[4,4,3,1]=>10
[4,4,2,2]=>9
[4,4,2,1,1]=>8
[4,4,1,1,1,1]=>5
[4,3,3,2]=>8
[4,3,3,1,1]=>7
[4,3,2,2,1]=>6
[4,3,2,1,1,1]=>7
[4,3,1,1,1,1,1]=>6
[4,2,2,2,2]=>5
[4,2,2,2,1,1]=>4
[4,2,2,1,1,1,1]=>5
[4,2,1,1,1,1,1,1]=>5
[4,1,1,1,1,1,1,1,1]=>3
[3,3,3,3]=>5
[3,3,3,2,1]=>6
[3,3,3,1,1,1]=>4
[3,3,2,2,2]=>4
[3,3,2,2,1,1]=>3
[3,3,2,1,1,1,1]=>4
[3,3,1,1,1,1,1,1]=>4
[3,2,2,2,2,1]=>4
[3,2,2,2,1,1,1]=>3
[3,2,2,1,1,1,1,1]=>3
[3,2,1,1,1,1,1,1,1]=>4
[3,1,1,1,1,1,1,1,1,1]=>3
[2,2,2,2,2,2]=>3
[2,2,2,2,2,1,1]=>2
[2,2,2,2,1,1,1,1]=>2
[2,2,2,1,1,1,1,1,1]=>2
[2,2,1,1,1,1,1,1,1,1]=>2
[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[13]=>2
[12,1]=>3
[10,3]=>4
[9,2,2]=>5
[8,5]=>4
[8,4,1]=>5
[8,3,2]=>7
[8,3,1,1]=>6
[7,6]=>5
[7,5,1]=>6
[7,4,2]=>7
[7,3,3]=>6
[6,6,1]=>5
[6,5,2]=>7
[6,5,1,1]=>6
[6,4,3]=>9
[6,4,2,1]=>10
[6,3,2,2]=>8
[6,3,1,1,1,1]=>6
[6,2,2,1,1,1]=>5
[6,1,1,1,1,1,1,1]=>3
[5,5,3]=>8
[5,4,4]=>7
[5,4,3,1]=>13
[5,4,2,2]=>12
[5,4,2,1,1]=>11
[5,4,1,1,1,1]=>6
[5,3,3,2]=>11
[5,3,3,1,1]=>10
[5,3,2,2,1]=>9
[5,3,2,1,1,1]=>8
[5,3,1,1,1,1,1]=>6
[5,2,2,2,1,1]=>5
[5,2,2,1,1,1,1]=>5
[5,2,1,1,1,1,1,1]=>4
[4,4,4,1]=>8
[4,4,3,2]=>10
[4,4,3,1,1]=>9
[4,4,2,2,1]=>8
[4,3,3,3]=>7
[4,3,3,2,1]=>7
[3,3,3,3,1]=>6
[3,3,3,2,2]=>5
[3,3,2,2,2,1]=>4
[3,3,2,1,1,1,1,1]=>4
[3,2,2,2,2,2]=>4
[3,2,2,2,2,1,1]=>3
[3,1,1,1,1,1,1,1,1,1,1]=>3
[2,2,2,2,2,2,1]=>3
[2,2,2,2,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,1,1,1]=>1
[14]=>2
[13,1]=>3
[12,2]=>4
[12,1,1]=>3
[9,5]=>4
[8,6]=>5
[8,5,1]=>5
[8,4,2]=>7
[8,3,1,1,1]=>5
[7,7]=>4
[7,5,2]=>7
[7,4,3]=>7
[6,6,2]=>6
[6,6,1,1]=>5
[6,5,3]=>9
[6,5,1,1,1]=>8
[6,4,4]=>8
[6,4,2,2]=>11
[6,2,2,2,2]=>7
[6,1,1,1,1,1,1,1,1]=>3
[5,5,4]=>7
[5,5,1,1,1,1]=>6
[5,4,3,2]=>14
[5,4,3,1,1]=>13
[5,4,2,2,1]=>12
[5,4,2,1,1,1]=>9
[5,4,1,1,1,1,1]=>6
[5,3,3,3]=>9
[5,3,3,2,1]=>11
[5,3,2,2,2]=>8
[5,3,2,2,1,1]=>7
[5,3,2,1,1,1,1]=>8
[5,3,1,1,1,1,1,1]=>6
[5,2,2,2,2,1]=>5
[5,2,2,1,1,1,1,1]=>5
[4,4,4,2]=>9
[4,4,4,1,1]=>8
[4,4,3,3]=>8
[4,4,3,2,1]=>10
[4,3,2,2,2,1]=>6
[3,3,3,3,2]=>6
[3,3,3,3,1,1]=>5
[3,3,3,2,2,1]=>4
[3,3,2,2,2,2]=>4
[3,3,1,1,1,1,1,1,1,1]=>4
[3,2,2,2,2,1,1,1]=>3
[2,2,2,2,2,2,2]=>3
[1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>1
[15]=>2
[14,1]=>3
[12,3]=>4
[11,2,2]=>5
[9,6]=>4
[9,5,1]=>5
[8,7]=>5
[8,5,2]=>6
[7,5,3]=>8
[6,6,3]=>7
[6,5,4]=>9
[6,5,1,1,1,1]=>8
[6,4,3,1,1]=>13
[6,3,3,3]=>9
[6,3,1,1,1,1,1,1]=>5
[6,2,2,2,2,1]=>7
[5,5,5]=>6
[5,4,3,3]=>11
[5,4,3,2,1]=>15
[5,4,3,1,1,1]=>10
[5,3,2,2,2,1]=>7
[5,3,2,2,1,1,1]=>7
[5,3,1,1,1,1,1,1,1]=>6
[4,4,4,3]=>8
[4,4,4,1,1,1]=>7
[4,3,3,3,2]=>7
[3,3,3,3,3]=>5
[3,3,3,3,2,1]=>6
[3,3,3,2,2,2]=>4
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>1
[16]=>2
[15,1]=>3
[12,4]=>4
[12,1,1,1,1]=>3
[10,6]=>4
[8,8]=>4
[8,6,2]=>7
[8,5,3]=>7
[7,6,3]=>7
[7,5,3,1]=>10
[6,6,4]=>8
[6,6,2,2]=>8
[6,5,5]=>7
[6,4,3,3]=>12
[5,5,3,3]=>11
[5,5,2,2,2]=>10
[5,4,4,3]=>10
[5,4,3,2,1,1]=>11
[5,4,2,2,2,1]=>8
[4,4,4,4]=>7
[4,4,4,2,2]=>9
[4,4,3,3,2]=>8
[4,3,3,3,3]=>6
[4,3,3,3,2,1]=>7
[3,3,3,3,2,2]=>5
[3,3,3,3,1,1,1,1]=>4
[3,3,2,2,2,2,2]=>4
[2,2,2,2,2,2,2,2]=>3
[2,2,2,2,2,2,1,1,1,1]=>2
[2,2,2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>1
[17]=>2
[9,8]=>5
[8,8,1]=>5
[8,6,3]=>7
[7,5,3,2]=>12
[6,5,3,3]=>13
[6,5,2,2,2]=>12
[6,4,4,3]=>12
[6,4,4,1,1,1]=>11
[6,3,3,3,2]=>11
[6,3,3,3,1,1]=>10
[5,5,4,3]=>11
[5,5,4,1,1,1]=>10
[5,5,2,2,2,1]=>9
[5,4,4,4]=>9
[5,4,3,2,2,1]=>9
[5,3,3,3,2,1]=>8
[4,4,4,3,2]=>10
[4,4,4,3,1,1]=>9
[4,4,4,2,2,1]=>8
[4,4,3,3,3]=>7
[3,3,3,3,3,2]=>6
[3,2,2,2,2,2,2,2]=>4
[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>3
[4,4,4,3,2,1]=>10
[5,4,3,3,2,1]=>9
[6,3,3,3,2,1]=>11
[6,5,2,2,2,1]=>12
[5,5,3,3,1,1]=>12
[6,5,4,1,1,1]=>13
[5,5,3,3,2]=>13
[5,5,4,2,2]=>14
[6,4,4,2,2]=>15
[6,5,4,3]=>14
[4,4,4,3,3]=>8
[4,4,4,4,2]=>9
[5,5,4,4]=>9
[6,4,4,4]=>10
[2,2,2,2,2,2,2,2,2]=>3
[3,3,3,3,3,3]=>5
[18]=>2
[6,2,2,2,2,2,2]=>5
[6,6,6]=>6
[4,2,2,2,2,2,2,2]=>5
[10,4,4]=>6
[9,6,3]=>6
[8,6,4]=>8
[10,8]=>5
[3,3,3,3,1,1,1,1,1,1]=>4
[9,9]=>4
[7,7,1,1,1,1]=>6
[5,4,4,3,2,1]=>11
[5,5,3,3,2,1]=>12
[5,5,4,2,2,1]=>13
[6,4,4,2,2,1]=>14
[5,5,4,3,1,1]=>14
[6,4,4,3,1,1]=>15
[6,5,3,3,1,1]=>16
[5,5,4,3,2]=>15
[6,4,4,3,2]=>16
[6,5,3,3,2]=>17
[6,5,4,2,2]=>18
[6,5,4,3,1]=>19
[6,5,4,1,1,1,1]=>10
[4,4,4,4,3]=>8
[4,3,3,3,3,3]=>6
[19]=>2
[7,2,2,2,2,2,2]=>6
[7,6,6]=>7
[5,2,2,2,2,2,2,2]=>5
[13,6]=>4
[11,4,4]=>6
[9,6,4]=>7
[8,5,4,2]=>11
[8,5,5,1]=>8
[5,5,4,3,2,1]=>15
[6,4,4,3,2,1]=>16
[6,5,3,3,2,1]=>17
[6,5,4,2,2,1]=>18
[6,5,4,3,1,1]=>19
[6,5,4,3,2]=>20
[6,5,2,2,2,2,1]=>8
[6,5,4,2,1,1,1]=>14
[6,6,2,2,2,2]=>10
[7,5,4,3,1]=>18
[2,2,2,2,2,2,2,2,2,2]=>3
[3,3,3,3,3,3,2]=>6
[4,4,3,3,3,3]=>6
[4,4,4,4,4]=>7
[5,5,5,5]=>8
[20]=>2
[10,10]=>4
[8,2,2,2,2,2,2]=>7
[8,6,4,2]=>11
[8,6,6]=>8
[10,6,4]=>7
[9,8,3]=>7
[6,6,6,2]=>9
[10,7,3]=>6
[9,7,4]=>7
[9,5,5,1]=>7
[6,5,4,3,2,1]=>21
[6,3,3,3,3,2,1]=>8
[6,5,3,2,2,2,1]=>11
[6,5,4,3,1,1,1]=>15
[7,6,2,2,2,2]=>12
[6,6,5,4]=>11
[3,3,3,3,3,3,3]=>5
[4,4,4,3,3,3]=>7
[21]=>2
[11,7,3]=>6
[5,4,2,2,2,2,2,2]=>8
[11,10]=>5
[13,4,4]=>6
[7,6,6,2]=>9
[4,4,4,4,3,2,1]=>10
[6,4,3,3,3,2,1]=>10
[6,5,4,2,2,2,1]=>12
[6,5,4,3,2,1,1]=>16
[4,4,4,4,3,3]=>8
[8,6,2,2,2,2]=>11
[22]=>2
[9,6,4,3]=>11
[8,7,7]=>7
[5,4,4,4,3,2,1]=>11
[6,5,3,3,3,2,1]=>11
[6,5,4,3,2,2,1]=>13
[15,2,2,2,2]=>5
[9,6,5,3]=>11
[8,6,5,3,1]=>15
[6,4,4,4,3,2,1]=>12
[6,5,4,3,3,2,1]=>12
[3,3,3,3,3,3,3,3]=>5
[4,4,4,4,4,4]=>7
[6,6,6,6]=>8
[24]=>2
[11,7,5,1]=>8
[9,7,5,3]=>11
[8,8,8]=>6
[17,7]=>4
[12,9,3]=>6
[5,5,5,4,3,2,1]=>15
[6,5,4,4,3,2,1]=>13
[7,6,6,6]=>9
[5,4,4,4,2,2,2,2]=>7
[13,12]=>5
[15,5,5]=>6
[9,7,5,3,1]=>13
[10,7,5,3]=>10
[3,3,3,3,3,1,1,1,1,1,1,1,1,1,1]=>4
[5,5,5,5,5]=>9
[12,10,3]=>7
[6,5,5,4,3,2,1]=>16
[6,6,4,3,3,2,2]=>13
[8,6,6,6]=>10
[9,7,5,4,1]=>13
[16,8,2]=>6
[6,6,5,4,3,2,1]=>21
[7,6,5,4,3,2]=>27
[3,3,3,3,3,3,3,3,3]=>5
[15,6,6]=>6
[7,6,5,4,3,2,1]=>28
[6,6,6,4,3,3]=>17
[4,3,3,3,3,3,3,3,3]=>6
[7,6,5,4,3,1,1,1]=>21
[10,7,6,4,1]=>12
[9,7,6,4,2]=>16
[10,8,5,4,1]=>11
[15,14]=>5
[7,6,5,4,3,2,1,1]=>22
[7,6,5,4,2,2,2,1]=>17
[10,8,6,4,1]=>12
[6,6,6,6,6]=>10
[15,15]=>4
[5,5,5,5,5,5]=>9
[6,6,6,6,3,3]=>15
[10,10,10]=>6
[9,7,5,5,3,1]=>20
[7,6,5,4,3,2,2,1]=>18
[7,6,5,3,3,3,2,1]=>15
[11,8,6,4,1]=>11
[10,8,6,4,2]=>14
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>3
[7,6,6,6,6]=>11
[7,6,5,4,3,3,2,1]=>16
[7,6,4,4,4,3,2,1]=>15
[11,8,6,5,1]=>12
[10,10,9,2]=>9
[14,9,8]=>7
[4,4,4,4,4,4,4,4]=>7
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>3
[7,6,5,4,4,3,2,1]=>16
[7,5,5,5,4,3,2,1]=>17
[16,16]=>4
[10,10,10,2]=>8
[16,8,4,2,2]=>11
[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>4
[5,4,4,4,4,4,4,4]=>8
[7,6,5,5,4,3,2,1]=>18
[6,6,6,5,4,3,2,1]=>21
[22,7,4]=>6
[12,12,4,3,2]=>13
[4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>5
[7,6,6,5,4,3,2,1]=>22
[12,9,7,5,1]=>11
[7,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>5
[7,7,6,5,4,3,2,1]=>28
[13,9,7,5,1]=>11
[18,18]=>4
[24,12]=>4
[11,9,7,5,3,1]=>16
[11,8,7,5,4,1]=>17
[8,7,6,5,4,3,2,1]=>36
[8,7,7,7,7]=>11
[7,6,2,2,2,2,2,2,2,2,2,2,2,2]=>8
[7,6,6,6,6,6]=>13
[8,7,6,5,4,3,2,1,1]=>29
[8,7,6,5,4,3,2,2,1]=>24
[8,7,6,5,4,3,3,2,1]=>21
[10,10,10,10]=>8
[12,12,12,4]=>8
[8,7,6,5,4,4,3,2,1]=>20
[11,9,7,5,5,3]=>20
[4,4,4,4,4,4,4,4,4,4]=>7
[14,14,8,4]=>8
[7,6,6,6,2,2,2,2,2,2,2,2]=>12
[8,7,6,5,5,4,3,2,1]=>21
[9,9,9,9,3,3]=>13
[8,7,6,6,5,4,3,2,1]=>24
[10,10,10,5,5,2]=>14
[16,10,8,8]=>10
[26,9,7]=>7
[8,7,7,6,5,4,3,2,1]=>29
[8,8,7,6,5,4,3,2,1]=>36
[18,18,9]=>6
[9,8,7,6,5,4,3,2,1]=>45
[11,9,7,7,5,3,3]=>27
[48]=>2
[7,6,6,6,6,6,6,6]=>12
[22,9,8,5,5]=>13
[6,6,6,6,6,6,6,3,3,2]=>17
[27,14,9]=>6
[17,14,13,8]=>9
[5,5,5,5,5,5,5,5,5,5,5]=>9
[27,20,8]=>6
[26,13,7,7,2]=>10
[31,12,10,4]=>9
[6,6,6,6,6,6,6,6,6,6]=>11
[5,5,5,5,5,5,5,5,5,5,5,5]=>9
[12,12,12,12,12]=>10
[12,12,12,12,11,4]=>13
[12,12,12,12,12,4]=>12
[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>4
[11,11,11,11,11,10]=>13
[11,11,11,11,11,11]=>12
[16,14,9,9,9,9]=>14
[8,8,8,8,8,8,8,8,4,2]=>20
[24,24,24]=>6
[16,16,16,16,8,4,2]=>15
[12,12,12,12,12,12,4,4]=>17
[22,20,20,12,8]=>12
[20,20,8,4,4,4,4,4,4,4,4,4]=>13
[33,32,9,9,5]=>11
[18,18,18,18,18]=>10
[18,18,18,18,9,9]=>12
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3]=>15
[56,17,11,10,5]=>11
[33,26,23,12,9]=>10
[22,22,22,10,10,9,4,4]=>17
[22,22,22,10,10,10,4,4]=>16
[12,12,12,12,12,12,12,12,4,3,2]=>31
[24,24,24,24,14]=>10
[76,22,9,6]=>8
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]=>9
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]=>9
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>11
[12,12,12,12,12,12,12,12,12,12]=>20
[24,24,24,24,24]=>10
[12,12,12,12,12,12,12,12,12,6,6,6,4,2]=>38
[54,48,18,10,8]=>11
[24,24,24,24,24,24]=>12
[37,33,20,20,13,10,10,10,7]=>22
[42,34,30,22,22,14,2]=>14
[54,52,34,18,11,7]=>13
[65,27,27,25,13,9,6,6]=>19
[18,18,18,18,18,18,18,18,18,18]=>20
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>11
[16,16,16,16,16,16,16,8,8,8,8,8,8,8,8,4,2]=>49
[58,38,38,38,30]=>10
[12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]=>23
[10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,2]=>21
[74,58,34,34,22,22,13,11,2]=>19
[61,48,48,48,45,22,12,2]=>18
[15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,5,5,3,3]=>40
[98,62,36,26,14,14,14,14,14,14,12,2]=>26
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,13,2]=>30
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,2]=>29
[74,74,26,26,26,26,12,12,12,12,12,12,6,6,4,4,3,3,3,3]=>45
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>11
[64,57,40,39,28,23,19,19,16,9,8,8,8,8,8,8,6,6]=>42
[70,70,46,28,22,22,10,9,9,9,9,8,8,8,8,8,7,7,7,3,3,3]=>38
[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,7,7,7,7,7,2]=>41
[170,92,36,28,27,24,20,14,13,10,8,8]=>28
[12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,6,6,6,6,4,4,4,3,3]=>34
[145,83,62,44,44,42,19,16,16,10,8]=>26
[98,98,37,37,37,37,24,24,24,24,24,24,24,24,10,10,8,8]=>39
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>11
[11,9,7,6,5,3,1]=>24
[13,11,9,7,5,3,1]=>19
[13,11,9,7,7,5,3,1]=>26
[17,13,11,9,7,5,1]=>17
[15,13,11,9,7,5,3,1]=>22
[29,23,19,17,13,11,7,1]=>17
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Description
The diagonal inversion number of an integer partition.
The dinv of a partition is the number of cells $c$ in the diagram of an integer partition $\lambda$ for which $\operatorname{arm}(c)-\operatorname{leg}(c) \in \{0,1\}$.
See also exercise 3.19 of [2].
This statistic is equidistributed with the length of the partition, see [3].
The dinv of a partition is the number of cells $c$ in the diagram of an integer partition $\lambda$ for which $\operatorname{arm}(c)-\operatorname{leg}(c) \in \{0,1\}$.
See also exercise 3.19 of [2].
This statistic is equidistributed with the length of the partition, see [3].
References
[1] Lee, K., Li, L., Loehr, N. A. A Combinatorial Approach to the Symmetry of $q,t$-Catalan Numbers arXiv:1602.01126
[2] Haglund, J. The $q$,$t$-Catalan numbers and the space of diagonal harmonics MathSciNet:2371044
[3] Robin Why are the dinv-statistic and the partition length equidistributed? MathOverflow:131484
[2] Haglund, J. The $q$,$t$-Catalan numbers and the space of diagonal harmonics MathSciNet:2371044
[3] Robin Why are the dinv-statistic and the partition length equidistributed? MathOverflow:131484
Code
def statistic(P):
return sum(1 for c in P.cells() if P.arm_length(*c) - P.leg_length(*c) in [0,1])
Created
Feb 06, 2016 at 17:13 by Christian Stump
Updated
Jan 15, 2024 at 12:24 by Martin Rubey
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