Values
=>
Cc0013;cc-rep
([2],3)=>3
([1,1],3)=>3
([2],4)=>3
([1,1],4)=>3
([2],5)=>3
([1,1],5)=>3
([2],6)=>3
([1,1],6)=>3
([3,1],3)=>5
([2,1,1],3)=>5
([3],4)=>4
([2,1],4)=>5
([1,1,1],4)=>4
([3],5)=>4
([2,1],5)=>5
([1,1,1],5)=>4
([3],6)=>4
([2,1],6)=>5
([1,1,1],6)=>4
([4,2],3)=>6
([3,1,1],3)=>7
([2,2,1,1],3)=>6
([4,1],4)=>7
([2,2],4)=>6
([3,1,1],4)=>8
([2,1,1,1],4)=>7
([4],5)=>5
([3,1],5)=>7
([2,2],5)=>6
([2,1,1],5)=>7
([1,1,1,1],5)=>5
([4],6)=>5
([3,1],6)=>7
([2,2],6)=>6
([2,1,1],6)=>7
([1,1,1,1],6)=>5
([5,3,1],3)=>9
([4,2,1,1],3)=>10
([3,2,2,1,1],3)=>9
([5,2],4)=>9
([4,1,1],4)=>10
([3,2,1],4)=>10
([3,1,1,1],4)=>10
([2,2,1,1,1],4)=>9
([5,1],5)=>9
([3,2],5)=>9
([4,1,1],5)=>11
([2,2,1],5)=>9
([3,1,1,1],5)=>11
([2,1,1,1,1],5)=>9
([5],6)=>6
([4,1],6)=>9
([3,2],6)=>9
([3,1,1],6)=>10
([2,2,1],6)=>9
([2,1,1,1],6)=>9
([1,1,1,1,1],6)=>6
([5,3,1,1],3)=>12
([4,2,2,1,1],3)=>12
([6,3],4)=>10
([5,2,1],4)=>14
([4,1,1,1],4)=>13
([4,2,2],4)=>13
([3,3,1,1],4)=>13
([3,2,1,1,1],4)=>14
([2,2,2,1,1,1],4)=>10
([6,2],5)=>12
([5,1,1],5)=>13
([3,3],5)=>10
([4,2,1],5)=>15
([4,1,1,1],5)=>14
([2,2,2],5)=>10
([3,2,1,1],5)=>15
([3,1,1,1,1],5)=>13
([2,2,1,1,1,1],5)=>12
([6,1],6)=>11
([4,2],6)=>12
([5,1,1],6)=>14
([3,3],6)=>10
([3,2,1],6)=>14
([4,1,1,1],6)=>15
([2,2,2],6)=>10
([2,2,1,1],6)=>12
([3,1,1,1,1],6)=>14
([2,1,1,1,1,1],6)=>11
([7,2],6)=>15
([6,1,1],6)=>16
([4,3],6)=>14
([5,2,1],6)=>20
([5,1,1,1],6)=>18
([3,3,1],6)=>16
([3,2,2],6)=>16
([4,2,1,1],6)=>22
([4,1,1,1,1],6)=>18
([2,2,2,1],6)=>14
([3,2,1,1,1],6)=>20
([3,1,1,1,1,1],6)=>16
([2,2,1,1,1,1,1],6)=>15
([1],2)=>2
([2,1],2)=>3
([3,2,1],2)=>4
([4,3,2,1],2)=>5
([1],3)=>2
([1],4)=>2
([5,2,2],4)=>16
([3,3,1,1,1],4)=>16
([5,2,1,1,1],4)=>20
([4,3,2,1],4)=>18
([6,3,1,1],4)=>20
([4,2,2,1,1,1],4)=>20
([1],5)=>2
([5,1,1,1],5)=>17
([4,3,1],5)=>17
([4,2,1,1],5)=>20
([4,1,1,1,1],5)=>17
([3,2,2,1],5)=>17
([6,2,1],5)=>19
([5,2,2],5)=>19
([5,1,1,1,1],5)=>21
([3,3,1,1,1],5)=>19
([3,2,1,1,1,1],5)=>19
([7,3],5)=>14
([6,2,2],5)=>22
([6,2,1,1],5)=>26
([5,3,2],5)=>22
([5,2,2,1],5)=>27
([4,4,1,1],5)=>23
([4,3,1,1,1],5)=>27
([4,2,2,2],5)=>23
([4,2,1,1,1,1],5)=>26
([3,3,2,1,1],5)=>22
([3,3,1,1,1,1],5)=>22
([2,2,2,1,1,1,1],5)=>14
([7,3,1],5)=>23
([6,2,2,1],5)=>32
([5,2,2,2],5)=>29
([4,4,1,1,1],5)=>29
([4,3,1,1,1,1],5)=>32
([3,2,2,1,1,1,1],5)=>23
([1],6)=>2
([4,4],6)=>15
([3,3,2],6)=>19
([2,2,2,2],6)=>15
([6,1,1,1],6)=>21
([5,3,1],6)=>24
([5,2,1,1],6)=>27
([5,1,1,1,1],6)=>22
([4,3,1,1],6)=>26
([4,2,2,1],6)=>26
([4,2,1,1,1],6)=>27
([4,1,1,1,1,1],6)=>21
([3,3,3],6)=>20
([3,2,2,1,1],6)=>24
([7,2,1],6)=>24
([6,2,2],6)=>25
([6,1,1,1,1],6)=>26
([5,4,1],6)=>26
([5,3,1,1],6)=>33
([5,2,1,1,1],6)=>34
([5,1,1,1,1,1],6)=>26
([4,3,2,1],6)=>32
([4,2,2,1,1],6)=>33
([3,3,1,1,1,1],6)=>25
([3,2,2,2,1],6)=>26
([3,2,1,1,1,1,1],6)=>24
([8,3],6)=>18
([7,2,2],6)=>28
([7,2,1,1],6)=>33
([6,3,2],6)=>31
([6,2,2,1],6)=>36
([6,1,1,1,1,1],6)=>31
([5,2,2,2],6)=>33
([4,4,1,1,1],6)=>33
([4,3,3,1],6)=>34
([4,3,1,1,1,1],6)=>36
([4,2,1,1,1,1,1],6)=>33
([3,3,2,1,1,1],6)=>31
([3,3,1,1,1,1,1],6)=>28
([2,2,2,1,1,1,1,1],6)=>18
([1],7)=>2
([2],7)=>3
([1,1],7)=>3
([3],7)=>4
([2,1],7)=>5
([1,1,1],7)=>4
([4],7)=>5
([3,1],7)=>7
([2,2],7)=>6
([2,1,1],7)=>7
([1,1,1,1],7)=>5
([5],7)=>6
([4,1],7)=>9
([3,2],7)=>9
([3,1,1],7)=>10
([2,2,1],7)=>9
([2,1,1,1],7)=>9
([1,1,1,1,1],7)=>6
([6],7)=>7
([5,1],7)=>11
([4,2],7)=>12
([4,1,1],7)=>13
([3,3],7)=>10
([3,2,1],7)=>14
([3,1,1,1],7)=>13
([2,2,2],7)=>10
([2,2,1,1],7)=>12
([2,1,1,1,1],7)=>11
([1,1,1,1,1,1],7)=>7
([5,2],7)=>15
([4,3],7)=>14
([4,2,1],7)=>19
([3,3,1],7)=>16
([3,2,2],7)=>16
([3,2,1,1],7)=>19
([2,2,2,1],7)=>14
([2,2,1,1,1],7)=>15
([7,1],7)=>13
([6,1,1],7)=>17
([5,3],7)=>18
([5,1,1,1],7)=>19
([4,4],7)=>15
([4,3,1],7)=>23
([4,2,2],7)=>22
([4,1,1,1,1],7)=>19
([3,3,2],7)=>19
([3,3,1,1],7)=>22
([3,2,2,1],7)=>23
([3,1,1,1,1,1],7)=>17
([2,2,2,2],7)=>15
([2,2,2,1,1],7)=>18
([2,1,1,1,1,1,1],7)=>13
([7,1,1],7)=>19
([6,2,1],7)=>25
([6,1,1,1],7)=>22
([5,4],7)=>20
([5,2,1,1],7)=>29
([5,1,1,1,1],7)=>23
([4,4,1],7)=>25
([4,3,2],7)=>28
([4,2,1,1,1],7)=>29
([4,1,1,1,1,1],7)=>22
([3,3,3],7)=>20
([3,3,2,1],7)=>28
([3,2,2,2],7)=>25
([3,2,1,1,1,1],7)=>25
([3,1,1,1,1,1,1],7)=>19
([2,2,2,2,1],7)=>20
([8,2],7)=>18
([7,1,1,1],7)=>25
([6,3,1],7)=>31
([6,2,1,1],7)=>34
([6,1,1,1,1],7)=>27
([5,5],7)=>21
([5,3,1,1],7)=>36
([5,2,2,1],7)=>35
([5,2,1,1,1],7)=>36
([5,1,1,1,1,1],7)=>27
([4,4,2],7)=>31
([4,3,3],7)=>30
([4,3,1,1,1],7)=>35
([4,2,2,1,1],7)=>36
([4,2,1,1,1,1],7)=>34
([4,1,1,1,1,1,1],7)=>25
([3,3,3,1],7)=>30
([3,3,2,2],7)=>31
([3,2,2,1,1,1],7)=>31
([2,2,2,2,2],7)=>21
([2,2,1,1,1,1,1,1],7)=>18
([8,2,1],7)=>29
([7,2,2],7)=>31
([7,1,1,1,1],7)=>31
([6,4,1],7)=>35
([6,3,1,1],7)=>43
([6,2,1,1,1],7)=>43
([6,1,1,1,1,1],7)=>32
([5,4,1,1],7)=>40
([5,3,2,1],7)=>46
([5,3,1,1,1],7)=>45
([5,2,2,1,1],7)=>45
([5,2,1,1,1,1],7)=>43
([5,1,1,1,1,1,1],7)=>31
([4,4,3],7)=>34
([4,3,2,1,1],7)=>46
([4,2,2,2,1],7)=>40
([4,2,2,1,1,1],7)=>43
([3,3,3,2],7)=>34
([3,3,1,1,1,1,1],7)=>31
([3,2,2,2,1,1],7)=>35
([3,2,1,1,1,1,1,1],7)=>29
([1],8)=>2
([2],8)=>3
([1,1],8)=>3
([3],8)=>4
([2,1],8)=>5
([1,1,1],8)=>4
([4],8)=>5
([3,1],8)=>7
([2,2],8)=>6
([2,1,1],8)=>7
([1,1,1,1],8)=>5
([5],8)=>6
([4,1],8)=>9
([3,2],8)=>9
([3,1,1],8)=>10
([2,2,1],8)=>9
([2,1,1,1],8)=>9
([1,1,1,1,1],8)=>6
([6],8)=>7
([5,1],8)=>11
([4,2],8)=>12
([4,1,1],8)=>13
([3,3],8)=>10
([3,2,1],8)=>14
([3,1,1,1],8)=>13
([2,2,2],8)=>10
([2,2,1,1],8)=>12
([2,1,1,1,1],8)=>11
([1,1,1,1,1,1],8)=>7
([7],8)=>8
([6,1],8)=>13
([5,2],8)=>15
([5,1,1],8)=>16
([4,3],8)=>14
([4,2,1],8)=>19
([4,1,1,1],8)=>17
([3,3,1],8)=>16
([3,2,2],8)=>16
([3,2,1,1],8)=>19
([3,1,1,1,1],8)=>16
([2,2,2,1],8)=>14
([2,2,1,1,1],8)=>15
([2,1,1,1,1,1],8)=>13
([1,1,1,1,1,1,1],8)=>8
([6,2],8)=>18
([5,3],8)=>18
([5,2,1],8)=>24
([4,4],8)=>15
([4,3,1],8)=>23
([4,2,2],8)=>22
([4,2,1,1],8)=>26
([3,3,2],8)=>19
([3,3,1,1],8)=>22
([3,2,2,1],8)=>23
([3,2,1,1,1],8)=>24
([2,2,2,2],8)=>15
([2,2,2,1,1],8)=>18
([2,2,1,1,1,1],8)=>18
([8,1],8)=>15
([7,1,1],8)=>20
([6,3],8)=>22
([6,1,1,1],8)=>23
([5,4],8)=>20
([5,3,1],8)=>30
([5,2,2],8)=>28
([5,1,1,1,1],8)=>24
([4,4,1],8)=>25
([4,3,2],8)=>28
([4,3,1,1],8)=>32
([4,2,2,1],8)=>32
([4,1,1,1,1,1],8)=>23
([3,3,3],8)=>20
([3,3,2,1],8)=>28
([3,3,1,1,1],8)=>28
([3,2,2,2],8)=>25
([3,2,2,1,1],8)=>30
([3,1,1,1,1,1,1],8)=>20
([2,2,2,2,1],8)=>20
([2,2,2,1,1,1],8)=>22
([2,1,1,1,1,1,1,1],8)=>15
([8,1,1],8)=>22
([7,2,1],8)=>30
([7,1,1,1],8)=>26
([6,4],8)=>25
([6,2,1,1],8)=>36
([6,1,1,1,1],8)=>28
([5,5],8)=>21
([5,4,1],8)=>34
([5,3,2],8)=>37
([5,2,1,1,1],8)=>38
([5,1,1,1,1,1],8)=>28
([4,4,2],8)=>31
([4,4,1,1],8)=>35
([4,3,3],8)=>30
([4,3,2,1],8)=>42
([4,2,2,2],8)=>35
([4,2,1,1,1,1],8)=>36
([4,1,1,1,1,1,1],8)=>26
([3,3,3,1],8)=>30
([3,3,2,2],8)=>31
([3,3,2,1,1],8)=>37
([3,2,2,2,1],8)=>34
([3,2,1,1,1,1,1],8)=>30
([3,1,1,1,1,1,1,1],8)=>22
([2,2,2,2,2],8)=>21
([2,2,2,2,1,1],8)=>25
([9,2],8)=>21
([8,1,1,1],8)=>29
([7,3,1],8)=>38
([7,2,1,1],8)=>41
([7,1,1,1,1],8)=>32
([6,5],8)=>27
([6,3,1,1],8)=>46
([6,2,2,1],8)=>44
([6,2,1,1,1],8)=>45
([6,1,1,1,1,1],8)=>33
([5,5,1],8)=>36
([5,4,2],8)=>43
([5,3,3],8)=>40
([5,3,1,1,1],8)=>48
([5,2,2,1,1],8)=>48
([5,2,1,1,1,1],8)=>45
([5,1,1,1,1,1,1],8)=>32
([4,4,3],8)=>34
([4,4,2,1],8)=>47
([4,3,3,1],8)=>46
([4,3,2,2],8)=>47
([4,3,1,1,1,1],8)=>44
([4,2,2,1,1,1],8)=>46
([4,2,1,1,1,1,1],8)=>41
([4,1,1,1,1,1,1,1],8)=>29
([3,3,3,2],8)=>34
([3,3,3,1,1],8)=>40
([3,3,2,2,1],8)=>43
([3,2,2,2,2],8)=>36
([3,2,2,1,1,1,1],8)=>38
([2,2,2,2,2,1],8)=>27
([2,2,1,1,1,1,1,1,1],8)=>21
([1],9)=>2
([2],9)=>3
([1,1],9)=>3
([3],9)=>4
([2,1],9)=>5
([1,1,1],9)=>4
([4],9)=>5
([3,1],9)=>7
([2,2],9)=>6
([2,1,1],9)=>7
([1,1,1,1],9)=>5
([5],9)=>6
([4,1],9)=>9
([3,2],9)=>9
([3,1,1],9)=>10
([2,2,1],9)=>9
([2,1,1,1],9)=>9
([1,1,1,1,1],9)=>6
([6],9)=>7
([5,1],9)=>11
([4,2],9)=>12
([4,1,1],9)=>13
([3,3],9)=>10
([3,2,1],9)=>14
([3,1,1,1],9)=>13
([2,2,2],9)=>10
([2,2,1,1],9)=>12
([2,1,1,1,1],9)=>11
([1,1,1,1,1,1],9)=>7
([7],9)=>8
([6,1],9)=>13
([5,2],9)=>15
([5,1,1],9)=>16
([4,3],9)=>14
([4,2,1],9)=>19
([4,1,1,1],9)=>17
([3,3,1],9)=>16
([3,2,2],9)=>16
([3,2,1,1],9)=>19
([3,1,1,1,1],9)=>16
([2,2,2,1],9)=>14
([2,2,1,1,1],9)=>15
([2,1,1,1,1,1],9)=>13
([1,1,1,1,1,1,1],9)=>8
([8],9)=>9
([7,1],9)=>15
([6,2],9)=>18
([6,1,1],9)=>19
([5,3],9)=>18
([5,2,1],9)=>24
([5,1,1,1],9)=>21
([4,4],9)=>15
([4,3,1],9)=>23
([4,2,2],9)=>22
([4,2,1,1],9)=>26
([4,1,1,1,1],9)=>21
([3,3,2],9)=>19
([3,3,1,1],9)=>22
([3,2,2,1],9)=>23
([3,2,1,1,1],9)=>24
([3,1,1,1,1,1],9)=>19
([2,2,2,2],9)=>15
([2,2,2,1,1],9)=>18
([2,2,1,1,1,1],9)=>18
([2,1,1,1,1,1,1],9)=>15
([1,1,1,1,1,1,1,1],9)=>9
([7,2],9)=>21
([6,3],9)=>22
([6,2,1],9)=>29
([5,4],9)=>20
([5,3,1],9)=>30
([5,2,2],9)=>28
([5,2,1,1],9)=>33
([4,4,1],9)=>25
([4,3,2],9)=>28
([4,3,1,1],9)=>32
([4,2,2,1],9)=>32
([4,2,1,1,1],9)=>33
([3,3,3],9)=>20
([3,3,2,1],9)=>28
([3,3,1,1,1],9)=>28
([3,2,2,2],9)=>25
([3,2,2,1,1],9)=>30
([3,2,1,1,1,1],9)=>29
([2,2,2,2,1],9)=>20
([2,2,2,1,1,1],9)=>22
([2,2,1,1,1,1,1],9)=>21
([9,1],9)=>17
([8,1,1],9)=>23
([7,3],9)=>26
([7,1,1,1],9)=>27
([6,4],9)=>25
([6,3,1],9)=>37
([6,2,2],9)=>34
([6,1,1,1,1],9)=>29
([5,5],9)=>21
([5,4,1],9)=>34
([5,3,2],9)=>37
([5,3,1,1],9)=>42
([5,2,2,1],9)=>41
([5,1,1,1,1,1],9)=>29
([4,4,2],9)=>31
([4,4,1,1],9)=>35
([4,3,3],9)=>30
([4,3,2,1],9)=>42
([4,3,1,1,1],9)=>41
([4,2,2,2],9)=>35
([4,2,2,1,1],9)=>42
([4,1,1,1,1,1,1],9)=>27
([3,3,3,1],9)=>30
([3,3,2,2],9)=>31
([3,3,2,1,1],9)=>37
([3,3,1,1,1,1],9)=>34
([3,2,2,2,1],9)=>34
([3,2,2,1,1,1],9)=>37
([3,1,1,1,1,1,1,1],9)=>23
([2,2,2,2,2],9)=>21
([2,2,2,2,1,1],9)=>25
([2,2,2,1,1,1,1],9)=>26
([2,1,1,1,1,1,1,1,1],9)=>17
([9,1,1],9)=>25
([8,2,1],9)=>35
([8,1,1,1],9)=>30
([7,4],9)=>30
([7,2,1,1],9)=>43
([7,1,1,1,1],9)=>33
([6,5],9)=>27
([6,4,1],9)=>43
([6,3,2],9)=>46
([6,2,1,1,1],9)=>47
([6,1,1,1,1,1],9)=>34
([5,5,1],9)=>36
([5,4,2],9)=>43
([5,4,1,1],9)=>48
([5,3,3],9)=>40
([5,3,2,1],9)=>56
([5,2,2,2],9)=>45
([5,2,1,1,1,1],9)=>47
([5,1,1,1,1,1,1],9)=>33
([4,4,3],9)=>34
([4,4,2,1],9)=>47
([4,4,1,1,1],9)=>45
([4,3,3,1],9)=>46
([4,3,2,2],9)=>47
([4,3,2,1,1],9)=>56
([4,2,2,2,1],9)=>48
([4,2,1,1,1,1,1],9)=>43
([4,1,1,1,1,1,1,1],9)=>30
([3,3,3,2],9)=>34
([3,3,3,1,1],9)=>40
([3,3,2,2,1],9)=>43
([3,3,2,1,1,1],9)=>46
([3,2,2,2,2],9)=>36
([3,2,2,2,1,1],9)=>43
([3,2,1,1,1,1,1,1],9)=>35
([3,1,1,1,1,1,1,1,1],9)=>25
([2,2,2,2,2,1],9)=>27
([2,2,2,2,1,1,1],9)=>30
([1],10)=>2
([2],10)=>3
([1,1],10)=>3
([3],10)=>4
([2,1],10)=>5
([1,1,1],10)=>4
([4],10)=>5
([3,1],10)=>7
([2,2],10)=>6
([2,1,1],10)=>7
([1,1,1,1],10)=>5
([5],10)=>6
([4,1],10)=>9
([3,2],10)=>9
([3,1,1],10)=>10
([2,2,1],10)=>9
([2,1,1,1],10)=>9
([1,1,1,1,1],10)=>6
([6],10)=>7
([5,1],10)=>11
([4,2],10)=>12
([4,1,1],10)=>13
([3,3],10)=>10
([3,2,1],10)=>14
([3,1,1,1],10)=>13
([2,2,2],10)=>10
([2,2,1,1],10)=>12
([2,1,1,1,1],10)=>11
([1,1,1,1,1,1],10)=>7
([7],10)=>8
([6,1],10)=>13
([5,2],10)=>15
([5,1,1],10)=>16
([4,3],10)=>14
([4,2,1],10)=>19
([4,1,1,1],10)=>17
([3,3,1],10)=>16
([3,2,2],10)=>16
([3,2,1,1],10)=>19
([3,1,1,1,1],10)=>16
([2,2,2,1],10)=>14
([2,2,1,1,1],10)=>15
([2,1,1,1,1,1],10)=>13
([1,1,1,1,1,1,1],10)=>8
([8],10)=>9
([7,1],10)=>15
([6,2],10)=>18
([6,1,1],10)=>19
([5,3],10)=>18
([5,2,1],10)=>24
([5,1,1,1],10)=>21
([4,4],10)=>15
([4,3,1],10)=>23
([4,2,2],10)=>22
([4,2,1,1],10)=>26
([4,1,1,1,1],10)=>21
([3,3,2],10)=>19
([3,3,1,1],10)=>22
([3,2,2,1],10)=>23
([3,2,1,1,1],10)=>24
([3,1,1,1,1,1],10)=>19
([2,2,2,2],10)=>15
([2,2,2,1,1],10)=>18
([2,2,1,1,1,1],10)=>18
([2,1,1,1,1,1,1],10)=>15
([1,1,1,1,1,1,1,1],10)=>9
([9],10)=>10
([8,1],10)=>17
([7,2],10)=>21
([7,1,1],10)=>22
([6,3],10)=>22
([6,2,1],10)=>29
([6,1,1,1],10)=>25
([5,4],10)=>20
([5,3,1],10)=>30
([5,2,2],10)=>28
([5,2,1,1],10)=>33
([5,1,1,1,1],10)=>26
([4,4,1],10)=>25
([4,3,2],10)=>28
([4,3,1,1],10)=>32
([4,2,2,1],10)=>32
([4,2,1,1,1],10)=>33
([4,1,1,1,1,1],10)=>25
([3,3,3],10)=>20
([3,3,2,1],10)=>28
([3,3,1,1,1],10)=>28
([3,2,2,2],10)=>25
([3,2,2,1,1],10)=>30
([3,2,1,1,1,1],10)=>29
([3,1,1,1,1,1,1],10)=>22
([2,2,2,2,1],10)=>20
([2,2,2,1,1,1],10)=>22
([2,2,1,1,1,1,1],10)=>21
([2,1,1,1,1,1,1,1],10)=>17
([1,1,1,1,1,1,1,1,1],10)=>10
([8,2],10)=>24
([7,3],10)=>26
([7,2,1],10)=>34
([6,4],10)=>25
([6,3,1],10)=>37
([6,2,2],10)=>34
([6,2,1,1],10)=>40
([5,5],10)=>21
([5,4,1],10)=>34
([5,3,2],10)=>37
([5,3,1,1],10)=>42
([5,2,2,1],10)=>41
([5,2,1,1,1],10)=>42
([4,4,2],10)=>31
([4,4,1,1],10)=>35
([4,3,3],10)=>30
([4,3,2,1],10)=>42
([4,3,1,1,1],10)=>41
([4,2,2,2],10)=>35
([4,2,2,1,1],10)=>42
([4,2,1,1,1,1],10)=>40
([3,3,3,1],10)=>30
([3,3,2,2],10)=>31
([3,3,2,1,1],10)=>37
([3,3,1,1,1,1],10)=>34
([3,2,2,2,1],10)=>34
([3,2,2,1,1,1],10)=>37
([3,2,1,1,1,1,1],10)=>34
([2,2,2,2,2],10)=>21
([2,2,2,2,1,1],10)=>25
([2,2,2,1,1,1,1],10)=>26
([2,2,1,1,1,1,1,1],10)=>24
([10,1],10)=>19
([9,1,1],10)=>26
([8,3],10)=>30
([8,1,1,1],10)=>31
([7,4],10)=>30
([7,3,1],10)=>44
([7,2,2],10)=>40
([7,1,1,1,1],10)=>34
([6,5],10)=>27
([6,4,1],10)=>43
([6,3,2],10)=>46
([6,3,1,1],10)=>52
([6,2,2,1],10)=>50
([6,1,1,1,1,1],10)=>35
([5,5,1],10)=>36
([5,4,2],10)=>43
([5,4,1,1],10)=>48
([5,3,3],10)=>40
([5,3,2,1],10)=>56
([5,3,1,1,1],10)=>54
([5,2,2,2],10)=>45
([5,2,2,1,1],10)=>54
([5,1,1,1,1,1,1],10)=>34
([4,4,3],10)=>34
([4,4,2,1],10)=>47
([4,4,1,1,1],10)=>45
([4,3,3,1],10)=>46
([4,3,2,2],10)=>47
([4,3,2,1,1],10)=>56
([4,3,1,1,1,1],10)=>50
([4,2,2,2,1],10)=>48
([4,2,2,1,1,1],10)=>52
([4,1,1,1,1,1,1,1],10)=>31
([3,3,3,2],10)=>34
([3,3,3,1,1],10)=>40
([3,3,2,2,1],10)=>43
([3,3,2,1,1,1],10)=>46
([3,3,1,1,1,1,1],10)=>40
([3,2,2,2,2],10)=>36
([3,2,2,2,1,1],10)=>43
([3,2,2,1,1,1,1],10)=>44
([3,1,1,1,1,1,1,1,1],10)=>26
([2,2,2,2,2,1],10)=>27
([2,2,2,2,1,1,1],10)=>30
([2,2,2,1,1,1,1,1],10)=>30
([2,1,1,1,1,1,1,1,1,1],10)=>19
([1],11)=>2
([2],11)=>3
([1,1],11)=>3
([3],11)=>4
([2,1],11)=>5
([1,1,1],11)=>4
([4],11)=>5
([3,1],11)=>7
([2,2],11)=>6
([2,1,1],11)=>7
([1,1,1,1],11)=>5
([5],11)=>6
([4,1],11)=>9
([3,2],11)=>9
([3,1,1],11)=>10
([2,2,1],11)=>9
([2,1,1,1],11)=>9
([1,1,1,1,1],11)=>6
([6],11)=>7
([5,1],11)=>11
([4,2],11)=>12
([4,1,1],11)=>13
([3,3],11)=>10
([3,2,1],11)=>14
([3,1,1,1],11)=>13
([2,2,2],11)=>10
([2,2,1,1],11)=>12
([2,1,1,1,1],11)=>11
([1,1,1,1,1,1],11)=>7
([7],11)=>8
([6,1],11)=>13
([5,2],11)=>15
([5,1,1],11)=>16
([4,3],11)=>14
([4,2,1],11)=>19
([4,1,1,1],11)=>17
([3,3,1],11)=>16
([3,2,2],11)=>16
([3,2,1,1],11)=>19
([3,1,1,1,1],11)=>16
([2,2,2,1],11)=>14
([2,2,1,1,1],11)=>15
([2,1,1,1,1,1],11)=>13
([1,1,1,1,1,1,1],11)=>8
([8],11)=>9
([7,1],11)=>15
([6,2],11)=>18
([6,1,1],11)=>19
([5,3],11)=>18
([5,2,1],11)=>24
([5,1,1,1],11)=>21
([4,4],11)=>15
([4,3,1],11)=>23
([4,2,2],11)=>22
([4,2,1,1],11)=>26
([4,1,1,1,1],11)=>21
([3,3,2],11)=>19
([3,3,1,1],11)=>22
([3,2,2,1],11)=>23
([3,2,1,1,1],11)=>24
([3,1,1,1,1,1],11)=>19
([2,2,2,2],11)=>15
([2,2,2,1,1],11)=>18
([2,2,1,1,1,1],11)=>18
([2,1,1,1,1,1,1],11)=>15
([1,1,1,1,1,1,1,1],11)=>9
([9],11)=>10
([8,1],11)=>17
([7,2],11)=>21
([7,1,1],11)=>22
([6,3],11)=>22
([6,2,1],11)=>29
([6,1,1,1],11)=>25
([5,4],11)=>20
([5,3,1],11)=>30
([5,2,2],11)=>28
([5,2,1,1],11)=>33
([5,1,1,1,1],11)=>26
([4,4,1],11)=>25
([4,3,2],11)=>28
([4,3,1,1],11)=>32
([4,2,2,1],11)=>32
([4,2,1,1,1],11)=>33
([4,1,1,1,1,1],11)=>25
([3,3,3],11)=>20
([3,3,2,1],11)=>28
([3,3,1,1,1],11)=>28
([3,2,2,2],11)=>25
([3,2,2,1,1],11)=>30
([3,2,1,1,1,1],11)=>29
([3,1,1,1,1,1,1],11)=>22
([2,2,2,2,1],11)=>20
([2,2,2,1,1,1],11)=>22
([2,2,1,1,1,1,1],11)=>21
([2,1,1,1,1,1,1,1],11)=>17
([1,1,1,1,1,1,1,1,1],11)=>10
([10],11)=>11
([9,1],11)=>19
([8,2],11)=>24
([8,1,1],11)=>25
([7,3],11)=>26
([7,2,1],11)=>34
([7,1,1,1],11)=>29
([6,4],11)=>25
([6,3,1],11)=>37
([6,2,2],11)=>34
([6,2,1,1],11)=>40
([6,1,1,1,1],11)=>31
([5,5],11)=>21
([5,4,1],11)=>34
([5,3,2],11)=>37
([5,3,1,1],11)=>42
([5,2,2,1],11)=>41
([5,2,1,1,1],11)=>42
([5,1,1,1,1,1],11)=>31
([4,4,2],11)=>31
([4,4,1,1],11)=>35
([4,3,3],11)=>30
([4,3,2,1],11)=>42
([4,3,1,1,1],11)=>41
([4,2,2,2],11)=>35
([4,2,2,1,1],11)=>42
([4,2,1,1,1,1],11)=>40
([4,1,1,1,1,1,1],11)=>29
([3,3,3,1],11)=>30
([3,3,2,2],11)=>31
([3,3,2,1,1],11)=>37
([3,3,1,1,1,1],11)=>34
([3,2,2,2,1],11)=>34
([3,2,2,1,1,1],11)=>37
([3,2,1,1,1,1,1],11)=>34
([3,1,1,1,1,1,1,1],11)=>25
([2,2,2,2,2],11)=>21
([2,2,2,2,1,1],11)=>25
([2,2,2,1,1,1,1],11)=>26
([2,2,1,1,1,1,1,1],11)=>24
([2,1,1,1,1,1,1,1,1],11)=>19
([1,1,1,1,1,1,1,1,1,1],11)=>11
([9,2],11)=>27
([8,3],11)=>30
([8,2,1],11)=>39
([7,4],11)=>30
([7,3,1],11)=>44
([7,2,2],11)=>40
([7,2,1,1],11)=>47
([6,5],11)=>27
([6,4,1],11)=>43
([6,3,2],11)=>46
([6,3,1,1],11)=>52
([6,2,2,1],11)=>50
([6,2,1,1,1],11)=>51
([5,5,1],11)=>36
([5,4,2],11)=>43
([5,4,1,1],11)=>48
([5,3,3],11)=>40
([5,3,2,1],11)=>56
([5,3,1,1,1],11)=>54
([5,2,2,2],11)=>45
([5,2,2,1,1],11)=>54
([5,2,1,1,1,1],11)=>51
([4,4,3],11)=>34
([4,4,2,1],11)=>47
([4,4,1,1,1],11)=>45
([4,3,3,1],11)=>46
([4,3,2,2],11)=>47
([4,3,2,1,1],11)=>56
([4,3,1,1,1,1],11)=>50
([4,2,2,2,1],11)=>48
([4,2,2,1,1,1],11)=>52
([4,2,1,1,1,1,1],11)=>47
([3,3,3,2],11)=>34
([3,3,3,1,1],11)=>40
([3,3,2,2,1],11)=>43
([3,3,2,1,1,1],11)=>46
([3,3,1,1,1,1,1],11)=>40
([3,2,2,2,2],11)=>36
([3,2,2,2,1,1],11)=>43
([3,2,2,1,1,1,1],11)=>44
([3,2,1,1,1,1,1,1],11)=>39
([2,2,2,2,2,1],11)=>27
([2,2,2,2,1,1,1],11)=>30
([2,2,2,1,1,1,1,1],11)=>30
([2,2,1,1,1,1,1,1,1],11)=>27
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Description
The number of k-cores contained in the k-core.
Let $\lambda$ and $\mu$ be $k$-cores. Then $\lambda$ contains $\mu$ if and only if the Ferrers diagram of $\lambda$ contains the diagram of $\mu$. Each nonempty core trivially contains two other cores, the empty core and itself. The poset corresponding to containment is Young's lattice restricted to cores [1].
Let $\lambda$ and $\mu$ be $k$-cores. Then $\lambda$ contains $\mu$ if and only if the Ferrers diagram of $\lambda$ contains the diagram of $\mu$. Each nonempty core trivially contains two other cores, the empty core and itself. The poset corresponding to containment is Young's lattice restricted to cores [1].
References
[1] Lam, T., Lapointe, L., Morse, J., Schilling, A., Shimozono, M., Zabrocki, M. $k$-Schur functions and affine Schubert calculus arXiv:1301.3569
Code
def statistic(c):
a = 0
for m in range(c.size()+1):
for d in Cores(c.k(), size=m):
if c.contains(d):
a += 1
return a
Created
May 16, 2014 at 14:46 by Patrick Bjerke
Updated
Nov 16, 2017 at 11:39 by Martin Rubey
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