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Identifier
Values
=>
Cc0002;cc-rep
[]=>0 [1]=>1 [2]=>1 [1,1]=>1 [3]=>1 [2,1]=>1 [1,1,1]=>1 [4]=>1 [3,1]=>1 [2,2]=>2 [2,1,1]=>1 [1,1,1,1]=>1 [5]=>1 [4,1]=>1 [3,2]=>2 [3,1,1]=>1 [2,2,1]=>2 [2,1,1,1]=>1 [1,1,1,1,1]=>1 [6]=>1 [5,1]=>1 [4,2]=>2 [4,1,1]=>1 [3,3]=>2 [3,2,1]=>2 [3,1,1,1]=>1 [2,2,2]=>2 [2,2,1,1]=>2 [2,1,1,1,1]=>1 [1,1,1,1,1,1]=>1 [7]=>1 [6,1]=>1 [5,2]=>2 [5,1,1]=>1 [4,3]=>2 [4,2,1]=>2 [4,1,1,1]=>1 [3,3,1]=>2 [3,2,2]=>2 [3,2,1,1]=>2 [3,1,1,1,1]=>1 [2,2,2,1]=>2 [2,2,1,1,1]=>2 [2,1,1,1,1,1]=>1 [1,1,1,1,1,1,1]=>1 [8]=>1 [7,1]=>1 [6,2]=>2 [6,1,1]=>1 [5,3]=>2 [5,2,1]=>2 [5,1,1,1]=>1 [4,4]=>2 [4,3,1]=>2 [4,2,2]=>2 [4,2,1,1]=>2 [4,1,1,1,1]=>1 [3,3,2]=>2 [3,3,1,1]=>2 [3,2,2,1]=>2 [3,2,1,1,1]=>2 [3,1,1,1,1,1]=>1 [2,2,2,2]=>2 [2,2,2,1,1]=>2 [2,2,1,1,1,1]=>2 [2,1,1,1,1,1,1]=>1 [1,1,1,1,1,1,1,1]=>1 [9]=>1 [8,1]=>1 [7,2]=>2 [7,1,1]=>1 [6,3]=>2 [6,2,1]=>2 [6,1,1,1]=>1 [5,4]=>2 [5,3,1]=>2 [5,2,2]=>2 [5,2,1,1]=>2 [5,1,1,1,1]=>1 [4,4,1]=>2 [4,3,2]=>2 [4,3,1,1]=>2 [4,2,2,1]=>2 [4,2,1,1,1]=>2 [4,1,1,1,1,1]=>1 [3,3,3]=>3 [3,3,2,1]=>2 [3,3,1,1,1]=>2 [3,2,2,2]=>2 [3,2,2,1,1]=>2 [3,2,1,1,1,1]=>2 [3,1,1,1,1,1,1]=>1 [2,2,2,2,1]=>2 [2,2,2,1,1,1]=>2 [2,2,1,1,1,1,1]=>2 [2,1,1,1,1,1,1,1]=>1 [1,1,1,1,1,1,1,1,1]=>1 [10]=>1 [9,1]=>1 [8,2]=>2 [8,1,1]=>1 [7,3]=>2 [7,2,1]=>2 [7,1,1,1]=>1 [6,4]=>2 [6,3,1]=>2 [6,2,2]=>2 [6,2,1,1]=>2 [6,1,1,1,1]=>1 [5,5]=>2 [5,4,1]=>2 [5,3,2]=>2 [5,3,1,1]=>2 [5,2,2,1]=>2 [5,2,1,1,1]=>2 [5,1,1,1,1,1]=>1 [4,4,2]=>2 [4,4,1,1]=>2 [4,3,3]=>3 [4,3,2,1]=>2 [4,3,1,1,1]=>2 [4,2,2,2]=>2 [4,2,2,1,1]=>2 [4,2,1,1,1,1]=>2 [4,1,1,1,1,1,1]=>1 [3,3,3,1]=>3 [3,3,2,2]=>2 [3,3,2,1,1]=>2 [3,3,1,1,1,1]=>2 [3,2,2,2,1]=>2 [3,2,2,1,1,1]=>2 [3,2,1,1,1,1,1]=>2 [3,1,1,1,1,1,1,1]=>1 [2,2,2,2,2]=>2 [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]=>1 [1,1,1,1,1,1,1,1,1,1]=>1 [11]=>1 [10,1]=>1 [9,1,1]=>1 [8,3]=>2 [8,2,1]=>2 [8,1,1,1]=>1 [7,4]=>2 [7,2,2]=>2 [7,1,1,1,1]=>1 [6,5]=>2 [6,4,1]=>2 [6,3,2]=>2 [6,3,1,1]=>2 [6,2,2,1]=>2 [6,1,1,1,1,1]=>1 [5,5,1]=>2 [5,4,2]=>2 [5,4,1,1]=>2 [5,3,3]=>3 [5,3,2,1]=>2 [5,3,1,1,1]=>2 [5,2,2,2]=>2 [5,2,2,1,1]=>2 [5,2,1,1,1,1]=>2 [5,1,1,1,1,1,1]=>1 [4,4,3]=>3 [4,4,2,1]=>2 [4,4,1,1,1]=>2 [4,3,3,1]=>3 [4,3,2,2]=>2 [4,3,2,1,1]=>2 [4,3,1,1,1,1]=>2 [4,2,2,2,1]=>2 [4,1,1,1,1,1,1,1]=>1 [3,3,3,2]=>3 [3,3,3,1,1]=>3 [3,3,2,2,1]=>2 [3,3,1,1,1,1,1]=>2 [3,2,2,2,2]=>2 [3,2,2,2,1,1]=>2 [3,2,2,1,1,1,1]=>2 [3,2,1,1,1,1,1,1]=>2 [3,1,1,1,1,1,1,1,1]=>1 [2,2,2,2,2,1]=>2 [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]=>1 [1,1,1,1,1,1,1,1,1,1,1]=>1 [12]=>1 [11,1]=>1 [10,2]=>2 [10,1,1]=>1 [9,3]=>2 [8,4]=>2 [8,3,1]=>2 [8,2,2]=>2 [8,2,1,1]=>2 [8,1,1,1,1]=>1 [7,5]=>2 [7,4,1]=>2 [6,6]=>2 [6,5,1]=>2 [6,4,2]=>2 [6,4,1,1]=>2 [6,3,3]=>3 [6,3,1,1,1]=>2 [6,2,2,2]=>2 [6,2,2,1,1]=>2 [6,2,1,1,1,1]=>2 [6,1,1,1,1,1,1]=>1 [5,5,2]=>2 [5,5,1,1]=>2 [5,4,3]=>3 [5,4,2,1]=>2 [5,4,1,1,1]=>2 [5,3,3,1]=>3 [5,3,2,2]=>2 [5,3,2,1,1]=>2 [5,3,1,1,1,1]=>2 [5,2,2,2,1]=>2 [5,2,2,1,1,1]=>2 [5,2,1,1,1,1,1]=>2 [5,1,1,1,1,1,1,1]=>1 [4,4,4]=>3 [4,4,3,1]=>3 [4,4,2,2]=>2 [4,4,2,1,1]=>2 [4,3,3,2]=>3 [4,3,3,1,1]=>3 [4,3,2,2,1]=>2 [4,3,1,1,1,1,1]=>2 [3,3,3,3]=>3 [3,3,3,2,1]=>3 [3,3,2,2,2]=>2 [3,3,2,2,1,1]=>2 [3,3,1,1,1,1,1,1]=>2 [3,2,2,2,2,1]=>2 [3,2,2,1,1,1,1,1]=>2 [2,2,2,2,2,2]=>2 [2,2,2,2,2,1,1]=>2 [2,2,2,2,1,1,1,1]=>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 [13]=>1 [12,1]=>1 [10,3]=>2 [9,2,2]=>2 [8,5]=>2 [8,4,1]=>2 [8,3,2]=>2 [8,3,1,1]=>2 [7,6]=>2 [7,5,1]=>2 [7,4,2]=>2 [7,3,3]=>3 [6,6,1]=>2 [6,5,2]=>2 [6,5,1,1]=>2 [6,4,3]=>3 [6,4,2,1]=>2 [6,3,2,2]=>2 [6,3,1,1,1,1]=>2 [6,2,2,1,1,1]=>2 [6,1,1,1,1,1,1,1]=>1 [5,5,3]=>3 [5,4,4]=>3 [5,4,3,1]=>3 [5,4,2,2]=>2 [5,4,2,1,1]=>2 [5,4,1,1,1,1]=>2 [5,3,3,2]=>3 [5,3,3,1,1]=>3 [5,3,2,2,1]=>2 [5,3,2,1,1,1]=>2 [5,3,1,1,1,1,1]=>2 [5,2,2,2,1,1]=>2 [5,2,2,1,1,1,1]=>2 [5,2,1,1,1,1,1,1]=>2 [4,4,4,1]=>3 [4,4,3,2]=>3 [4,4,3,1,1]=>3 [4,4,2,2,1]=>2 [4,3,3,3]=>3 [4,3,3,2,1]=>3 [3,3,3,3,1]=>3 [3,3,3,2,2]=>3 [3,3,2,2,2,1]=>2 [3,3,2,1,1,1,1,1]=>2 [3,2,2,2,2,2]=>2 [3,2,2,2,2,1,1]=>2 [3,1,1,1,1,1,1,1,1,1,1]=>1 [2,2,2,2,2,2,1]=>2 [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]=>1 [13,1]=>1 [12,2]=>2 [12,1,1]=>1 [9,5]=>2 [8,6]=>2 [8,5,1]=>2 [8,4,2]=>2 [8,3,1,1,1]=>2 [7,7]=>2 [7,5,2]=>2 [7,4,3]=>3 [6,6,2]=>2 [6,6,1,1]=>2 [6,5,3]=>3 [6,5,1,1,1]=>2 [6,4,4]=>3 [6,4,2,2]=>2 [6,2,2,2,2]=>2 [6,1,1,1,1,1,1,1,1]=>1 [5,5,4]=>3 [5,5,1,1,1,1]=>2 [5,4,3,2]=>3 [5,4,3,1,1]=>3 [5,4,2,2,1]=>2 [5,4,2,1,1,1]=>2 [5,4,1,1,1,1,1]=>2 [5,3,3,3]=>3 [5,3,3,2,1]=>3 [5,3,2,2,2]=>2 [5,3,2,2,1,1]=>2 [5,3,2,1,1,1,1]=>2 [5,3,1,1,1,1,1,1]=>2 [5,2,2,2,2,1]=>2 [5,2,2,1,1,1,1,1]=>2 [4,4,4,2]=>3 [4,4,4,1,1]=>3 [4,4,3,3]=>3 [4,4,3,2,1]=>3 [4,3,2,2,2,1]=>2 [3,3,3,3,2]=>3 [3,3,3,3,1,1]=>3 [3,3,3,2,2,1]=>3 [3,3,2,2,2,2]=>2 [3,3,1,1,1,1,1,1,1,1]=>2 [3,2,2,2,2,1,1,1]=>2 [2,2,2,2,2,2,2]=>2 [1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>1 [15]=>1 [14,1]=>1 [12,3]=>2 [11,2,2]=>2 [9,6]=>2 [9,5,1]=>2 [8,7]=>2 [8,5,2]=>2 [7,5,3]=>3 [6,6,3]=>3 [6,5,4]=>3 [6,5,1,1,1,1]=>2 [6,4,3,1,1]=>3 [6,3,3,3]=>3 [6,3,1,1,1,1,1,1]=>2 [6,2,2,2,2,1]=>2 [5,5,5]=>3 [5,4,3,3]=>3 [5,4,3,2,1]=>3 [5,4,3,1,1,1]=>3 [5,3,2,2,2,1]=>2 [5,3,2,2,1,1,1]=>2 [5,3,1,1,1,1,1,1,1]=>2 [4,4,4,3]=>3 [4,4,4,1,1,1]=>3 [4,3,3,3,2]=>3 [3,3,3,3,3]=>3 [3,3,3,3,2,1]=>3 [3,3,3,2,2,2]=>3 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>1 [16]=>1 [15,1]=>1 [12,4]=>2 [12,1,1,1,1]=>1 [10,6]=>2 [8,8]=>2 [8,6,2]=>2 [8,5,3]=>3 [7,6,3]=>3 [7,5,3,1]=>3 [6,6,4]=>3 [6,6,2,2]=>2 [6,5,5]=>3 [6,4,3,3]=>3 [5,5,3,3]=>3 [5,5,2,2,2]=>2 [5,4,4,3]=>3 [5,4,3,2,1,1]=>3 [5,4,2,2,2,1]=>2 [4,4,4,4]=>4 [4,4,4,2,2]=>3 [4,4,3,3,2]=>3 [4,3,3,3,3]=>3 [4,3,3,3,2,1]=>3 [3,3,3,3,2,2]=>3 [3,3,3,3,1,1,1,1]=>3 [2,2,2,2,2,2,2,2]=>2 [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]=>1 [9,8]=>2 [8,8,1]=>2 [8,6,3]=>3 [7,5,3,2]=>3 [6,5,3,3]=>3 [6,5,2,2,2]=>2 [6,4,4,3]=>3 [6,4,4,1,1,1]=>3 [6,3,3,3,2]=>3 [6,3,3,3,1,1]=>3 [5,5,4,3]=>3 [5,5,4,1,1,1]=>3 [5,5,2,2,2,1]=>2 [5,4,4,4]=>4 [5,4,3,2,2,1]=>3 [5,3,3,3,2,1]=>3 [4,4,4,3,2]=>3 [4,4,4,3,1,1]=>3 [4,4,4,2,2,1]=>3 [4,4,3,3,3]=>3 [3,3,3,3,3,2]=>3 [3,2,2,2,2,2,2,2]=>2 [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>1 [4,4,4,3,2,1]=>3 [5,4,3,3,2,1]=>3 [6,3,3,3,2,1]=>3 [6,5,2,2,2,1]=>2 [5,5,3,3,1,1]=>3 [6,5,4,1,1,1]=>3 [5,5,3,3,2]=>3 [5,5,4,2,2]=>3 [6,4,4,2,2]=>3 [6,5,4,3]=>3 [4,4,4,3,3]=>3 [4,4,4,4,2]=>4 [5,5,4,4]=>4 [6,4,4,4]=>4 [2,2,2,2,2,2,2,2,2]=>2 [3,3,3,3,3,3]=>3 [18]=>1 [6,2,2,2,2,2,2]=>2 [6,6,6]=>3 [4,2,2,2,2,2,2,2]=>2 [10,4,4]=>3 [9,6,3]=>3 [8,6,4]=>3 [10,8]=>2 [3,3,3,3,1,1,1,1,1,1]=>3 [9,9]=>2 [7,7,1,1,1,1]=>2 [5,4,4,3,2,1]=>3 [5,5,3,3,2,1]=>3 [5,5,4,2,2,1]=>3 [6,4,4,2,2,1]=>3 [5,5,4,3,1,1]=>3 [6,4,4,3,1,1]=>3 [6,5,3,3,1,1]=>3 [5,5,4,3,2]=>3 [6,4,4,3,2]=>3 [6,5,3,3,2]=>3 [6,5,4,2,2]=>3 [6,5,4,3,1]=>3 [6,5,4,1,1,1,1]=>3 [4,4,4,4,3]=>4 [4,3,3,3,3,3]=>3 [19]=>1 [7,2,2,2,2,2,2]=>2 [7,6,6]=>3 [5,2,2,2,2,2,2,2]=>2 [13,6]=>2 [11,4,4]=>3 [9,6,4]=>3 [8,5,4,2]=>3 [8,5,5,1]=>3 [5,5,4,3,2,1]=>3 [6,4,4,3,2,1]=>3 [6,5,3,3,2,1]=>3 [6,5,4,2,2,1]=>3 [6,5,4,3,1,1]=>3 [6,5,4,3,2]=>3 [6,5,2,2,2,2,1]=>2 [6,5,4,2,1,1,1]=>3 [6,6,2,2,2,2]=>2 [7,5,4,3,1]=>3 [2,2,2,2,2,2,2,2,2,2]=>2 [3,3,3,3,3,3,2]=>3 [4,4,3,3,3,3]=>3 [4,4,4,4,4]=>4 [5,5,5,5]=>4 [20]=>1 [10,10]=>2 [8,2,2,2,2,2,2]=>2 [8,6,4,2]=>3 [8,6,6]=>3 [10,6,4]=>3 [9,8,3]=>3 [6,6,6,2]=>3 [10,7,3]=>3 [9,7,4]=>3 [9,5,5,1]=>3 [6,5,4,3,2,1]=>3 [6,3,3,3,3,2,1]=>3 [6,5,3,2,2,2,1]=>3 [6,5,4,3,1,1,1]=>3 [7,6,2,2,2,2]=>2 [6,6,5,4]=>4 [3,3,3,3,3,3,3]=>3 [4,4,4,3,3,3]=>3 [21]=>1 [11,7,3]=>3 [5,4,2,2,2,2,2,2]=>2 [11,10]=>2 [13,4,4]=>3 [7,6,6,2]=>3 [4,4,4,4,3,2,1]=>4 [6,4,3,3,3,2,1]=>3 [6,5,4,2,2,2,1]=>3 [6,5,4,3,2,1,1]=>3 [4,4,4,4,3,3]=>4 [8,6,2,2,2,2]=>2 [22]=>1 [9,6,4,3]=>3 [8,7,7]=>3 [5,4,4,4,3,2,1]=>4 [6,5,3,3,3,2,1]=>3 [6,5,4,3,2,2,1]=>3 [15,2,2,2,2]=>2 [9,6,5,3]=>3 [8,6,5,3,1]=>3 [6,4,4,4,3,2,1]=>4 [6,5,4,3,3,2,1]=>3 [3,3,3,3,3,3,3,3]=>3 [4,4,4,4,4,4]=>4 [6,6,6,6]=>4 [24]=>1 [11,7,5,1]=>3 [9,7,5,3]=>3 [8,8,8]=>3 [17,7]=>2 [12,9,3]=>3 [5,5,5,4,3,2,1]=>4 [6,5,4,4,3,2,1]=>4 [7,6,6,6]=>4 [5,4,4,4,2,2,2,2]=>4 [13,12]=>2 [15,5,5]=>3 [9,7,5,3,1]=>3 [10,7,5,3]=>3 [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1]=>3 [5,5,5,5,5]=>5 [12,10,3]=>3 [6,5,5,4,3,2,1]=>4 [6,6,4,3,3,2,2]=>3 [8,6,6,6]=>4 [9,7,5,4,1]=>4 [16,8,2]=>2 [6,6,5,4,3,2,1]=>4 [7,6,5,4,3,2]=>4 [3,3,3,3,3,3,3,3,3]=>3 [15,6,6]=>3 [7,6,5,4,3,2,1]=>4 [6,6,6,4,3,3]=>4 [4,3,3,3,3,3,3,3,3]=>3 [7,6,5,4,3,1,1,1]=>4 [10,7,6,4,1]=>4 [9,7,6,4,2]=>4 [10,8,5,4,1]=>4 [15,14]=>2 [7,6,5,4,3,2,1,1]=>4 [7,6,5,4,2,2,2,1]=>4 [10,8,6,4,1]=>4 [6,6,6,6,6]=>5 [15,15]=>2 [5,5,5,5,5,5]=>5 [6,6,6,6,3,3]=>4 [10,10,10]=>3 [9,7,5,5,3,1]=>4 [7,6,5,4,3,2,2,1]=>4 [7,6,5,3,3,3,2,1]=>3 [11,8,6,4,1]=>4 [10,8,6,4,2]=>4 [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>2 [7,6,6,6,6]=>5 [7,6,5,4,3,3,2,1]=>4 [7,6,4,4,4,3,2,1]=>4 [11,8,6,5,1]=>4 [10,10,9,2]=>3 [14,9,8]=>3 [4,4,4,4,4,4,4,4]=>4 [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>2 [7,6,5,4,4,3,2,1]=>4 [7,5,5,5,4,3,2,1]=>4 [16,16]=>2 [10,10,10,2]=>3 [16,8,4,2,2]=>3 [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>2 [5,4,4,4,4,4,4,4]=>4 [7,6,5,5,4,3,2,1]=>4 [6,6,6,5,4,3,2,1]=>4 [22,7,4]=>3 [12,12,4,3,2]=>3 [4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>2 [7,6,6,5,4,3,2,1]=>4 [12,9,7,5,1]=>4 [7,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>2 [7,7,6,5,4,3,2,1]=>4 [13,9,7,5,1]=>4 [18,18]=>2 [24,12]=>2 [11,9,7,5,3,1]=>4 [11,8,7,5,4,1]=>4 [8,7,6,5,4,3,2,1]=>4 [8,7,7,7,7]=>5 [7,6,2,2,2,2,2,2,2,2,2,2,2,2]=>2 [7,6,6,6,6,6]=>6 [8,7,6,5,4,3,2,1,1]=>4 [8,7,6,5,4,3,2,2,1]=>4 [8,7,6,5,4,3,3,2,1]=>4 [10,10,10,10]=>4 [12,12,12,4]=>4 [8,7,6,5,4,4,3,2,1]=>4 [11,9,7,5,5,3]=>5 [4,4,4,4,4,4,4,4,4,4]=>4 [14,14,8,4]=>4 [7,6,6,6,2,2,2,2,2,2,2,2]=>4 [8,7,6,5,5,4,3,2,1]=>5 [9,9,9,9,3,3]=>4 [8,7,6,6,5,4,3,2,1]=>5 [10,10,10,5,5,2]=>5 [16,10,8,8]=>4 [26,9,7]=>3 [8,7,7,6,5,4,3,2,1]=>5 [8,8,7,6,5,4,3,2,1]=>5 [18,18,9]=>3 [9,8,7,6,5,4,3,2,1]=>5 [11,9,7,7,5,3,3]=>5 [48]=>1 [7,6,6,6,6,6,6,6]=>6 [22,9,8,5,5]=>5 [6,6,6,6,6,6,6,3,3,2]=>6 [27,14,9]=>3 [17,14,13,8]=>4 [5,5,5,5,5,5,5,5,5,5,5]=>5 [27,20,8]=>3 [26,13,7,7,2]=>4 [31,12,10,4]=>4 [6,6,6,6,6,6,6,6,6,6]=>6 [5,5,5,5,5,5,5,5,5,5,5,5]=>5 [12,12,12,12,12]=>5 [12,12,12,12,11,4]=>5 [12,12,12,12,12,4]=>5 [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]=>2 [11,11,11,11,11,10]=>6 [11,11,11,11,11,11]=>6 [16,14,9,9,9,9]=>6 [8,8,8,8,8,8,8,8,4,2]=>8 [24,24,24]=>3 [16,16,16,16,8,4,2]=>5 [12,12,12,12,12,12,4,4]=>6 [22,20,20,12,8]=>5 [20,20,8,4,4,4,4,4,4,4,4,4]=>4 [33,32,9,9,5]=>5 [18,18,18,18,18]=>5 [18,18,18,18,9,9]=>6 [6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3]=>6 [56,17,11,10,5]=>5 [33,26,23,12,9]=>5 [22,22,22,10,10,9,4,4]=>6 [22,22,22,10,10,10,4,4]=>6 [12,12,12,12,12,12,12,12,4,3,2]=>8 [24,24,24,24,14]=>5 [76,22,9,6]=>4 [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]=>5 [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]=>5 [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>6 [12,12,12,12,12,12,12,12,12,12]=>10 [24,24,24,24,24]=>5 [12,12,12,12,12,12,12,12,12,6,6,6,4,2]=>9 [54,48,18,10,8]=>5 [24,24,24,24,24,24]=>6 [37,33,20,20,13,10,10,10,7]=>8 [42,34,30,22,22,14,2]=>6 [54,52,34,18,11,7]=>6 [65,27,27,25,13,9,6,6]=>6 [18,18,18,18,18,18,18,18,18,18]=>10 [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 [16,16,16,16,16,16,16,8,8,8,8,8,8,8,8,4,2]=>8 [58,38,38,38,30]=>5 [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]=>12 [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]=>10 [74,58,34,34,22,22,13,11,2]=>8 [61,48,48,48,45,22,12,2]=>7 [15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,5,5,3,3]=>15 [98,62,36,26,14,14,14,14,14,14,12,2]=>11 [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]=>14 [14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,2]=>14 [74,74,26,26,26,26,12,12,12,12,12,12,6,6,4,4,3,3,3,3]=>12 [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 [64,57,40,39,28,23,19,19,16,9,8,8,8,8,8,8,6,6]=>9 [70,70,46,28,22,22,10,9,9,9,9,8,8,8,8,8,7,7,7,3,3,3]=>9 [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]=>14 [170,92,36,28,27,24,20,14,13,10,8,8]=>10 [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]=>12 [145,83,62,44,44,42,19,16,16,10,8]=>10 [98,98,37,37,37,37,24,24,24,24,24,24,24,24,10,10,8,8]=>14 [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]=>6 [11,9,7,6,5,3,1]=>5 [13,11,9,7,5,3,1]=>5 [13,11,9,7,7,5,3,1]=>5 [17,13,11,9,7,5,1]=>5 [15,13,11,9,7,5,3,1]=>5 [29,23,19,17,13,11,7,1]=>7
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Description
The side length of the Durfee square of an integer partition.
Given a partition $\lambda = (\lambda_1,\ldots,\lambda_n)$, the Durfee square is the largest partition $(s^s)$ whose diagram fits inside the diagram of $\lambda$. In symbols, $s = \max\{ i \mid \lambda_i \geq i \}$.
This is also known as the Frobenius rank.
References
[1] wikipedia:Durfee_square
[2] Andrews, G. E., Eriksson, K. Integer partitions MathSciNet:2122332
Code
def statistic(p):
    s = 0
    while len(p) > s and p[s] >= s+1:
        s += 1
    return s

#CodeLanguage: Mathematica
SageForm[part_] := StringJoin["[", Riffle[ToString /@ part, ","], "]"]
ips = Join @@ (IntegerPartitions /@ Range[10]);
stat[p_] := Combinatorica`DurfeeSquare[p];
Print[StringJoin @@ 
   Table[StringJoin[SageForm[p], " => ", ToString[stat[p]], "\n"], {p,
      ips[[1 ;; 138]]}]];
Created
May 05, 2014 at 06:22 by Lahiru Kariyawasam
Updated
Oct 27, 2023 at 10:20 by Martin Rubey