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.
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
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
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