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Identifier
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].
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