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Identifier
Values
=>
Cc0019;cc-rep
[[1]]=>0 [[2]]=>1 [[3]]=>1 [[4]]=>1 [[1,1]]=>0 [[1,2]]=>0 [[2,2]]=>1 [[1],[2]]=>0 [[1,3]]=>0 [[2,3]]=>1 [[3,3]]=>1 [[1],[3]]=>1 [[2],[3]]=>2 [[1,4]]=>0 [[2,4]]=>1 [[3,4]]=>1 [[4,4]]=>1 [[1],[4]]=>1 [[2],[4]]=>2 [[3],[4]]=>2 [[1,1,1]]=>0 [[1,1,2]]=>0 [[1,2,2]]=>0 [[2,2,2]]=>1 [[1,1],[2]]=>0 [[1,2],[2]]=>1 [[1,1,3]]=>0 [[1,2,3]]=>0 [[1,3,3]]=>0 [[2,2,3]]=>1 [[2,3,3]]=>1 [[3,3,3]]=>1 [[1,1],[3]]=>1 [[1,2],[3]]=>1 [[1,3],[2]]=>1 [[1,3],[3]]=>2 [[2,2],[3]]=>2 [[2,3],[3]]=>3 [[1],[2],[3]]=>0 [[1,1,4]]=>0 [[1,2,4]]=>0 [[1,3,4]]=>0 [[1,4,4]]=>0 [[2,2,4]]=>1 [[2,3,4]]=>1 [[2,4,4]]=>1 [[3,3,4]]=>1 [[3,4,4]]=>1 [[4,4,4]]=>1 [[1,1],[4]]=>1 [[1,2],[4]]=>1 [[1,4],[2]]=>1 [[1,3],[4]]=>1 [[1,4],[3]]=>2 [[1,4],[4]]=>2 [[2,2],[4]]=>2 [[2,3],[4]]=>2 [[2,4],[3]]=>3 [[2,4],[4]]=>3 [[3,3],[4]]=>2 [[3,4],[4]]=>3 [[1],[2],[4]]=>1 [[1],[3],[4]]=>2 [[2],[3],[4]]=>3 [[1,1,1,1]]=>0 [[1,1,1,2]]=>0 [[1,1,2,2]]=>0 [[1,2,2,2]]=>0 [[2,2,2,2]]=>1 [[1,1,1],[2]]=>0 [[1,1,2],[2]]=>0 [[1,2,2],[2]]=>1 [[1,1],[2,2]]=>0 [[1,1,1,3]]=>0 [[1,1,2,3]]=>0 [[1,1,3,3]]=>0 [[1,2,2,3]]=>0 [[1,2,3,3]]=>0 [[1,3,3,3]]=>0 [[2,2,2,3]]=>1 [[2,2,3,3]]=>1 [[2,3,3,3]]=>1 [[3,3,3,3]]=>1 [[1,1,1],[3]]=>1 [[1,1,2],[3]]=>1 [[1,1,3],[2]]=>0 [[1,1,3],[3]]=>1 [[1,2,2],[3]]=>1 [[1,2,3],[2]]=>1 [[1,2,3],[3]]=>1 [[1,3,3],[2]]=>1 [[1,3,3],[3]]=>2 [[2,2,2],[3]]=>2 [[2,2,3],[3]]=>2 [[2,3,3],[3]]=>3 [[1,1],[2,3]]=>0 [[1,1],[3,3]]=>1 [[1,2],[2,3]]=>1 [[1,2],[3,3]]=>1 [[2,2],[3,3]]=>2 [[1,1],[2],[3]]=>0 [[1,2],[2],[3]]=>1 [[1,3],[2],[3]]=>1 [[1,1,1,4]]=>0 [[1,1,2,4]]=>0 [[1,1,3,4]]=>0 [[1,1,4,4]]=>0 [[1,2,2,4]]=>0 [[1,2,3,4]]=>0 [[1,2,4,4]]=>0 [[1,3,3,4]]=>0 [[1,3,4,4]]=>0 [[1,4,4,4]]=>0 [[2,2,2,4]]=>1 [[2,2,3,4]]=>1 [[2,2,4,4]]=>1 [[2,3,3,4]]=>1 [[2,3,4,4]]=>1 [[2,4,4,4]]=>1 [[3,3,3,4]]=>1 [[3,3,4,4]]=>1 [[3,4,4,4]]=>1 [[4,4,4,4]]=>1 [[1,1,1],[4]]=>1 [[1,1,2],[4]]=>1 [[1,1,4],[2]]=>0 [[1,1,3],[4]]=>1 [[1,1,4],[3]]=>1 [[1,1,4],[4]]=>1 [[1,2,2],[4]]=>1 [[1,2,4],[2]]=>1 [[1,2,3],[4]]=>1 [[1,2,4],[3]]=>1 [[1,3,4],[2]]=>1 [[1,2,4],[4]]=>1 [[1,4,4],[2]]=>1 [[1,3,3],[4]]=>1 [[1,3,4],[3]]=>2 [[1,3,4],[4]]=>1 [[1,4,4],[3]]=>2 [[1,4,4],[4]]=>2 [[2,2,2],[4]]=>2 [[2,2,3],[4]]=>2 [[2,2,4],[3]]=>2 [[2,2,4],[4]]=>2 [[2,3,3],[4]]=>2 [[2,3,4],[3]]=>3 [[2,3,4],[4]]=>2 [[2,4,4],[3]]=>3 [[2,4,4],[4]]=>3 [[3,3,3],[4]]=>2 [[3,3,4],[4]]=>2 [[3,4,4],[4]]=>3 [[1,1],[2,4]]=>0 [[1,1],[3,4]]=>1 [[1,1],[4,4]]=>1 [[1,2],[2,4]]=>1 [[1,2],[3,4]]=>2 [[1,3],[2,4]]=>1 [[1,2],[4,4]]=>1 [[1,3],[3,4]]=>2 [[1,3],[4,4]]=>1 [[2,2],[3,4]]=>2 [[2,2],[4,4]]=>2 [[2,3],[3,4]]=>3 [[2,3],[4,4]]=>2 [[3,3],[4,4]]=>2 [[1,1],[2],[4]]=>1 [[1,1],[3],[4]]=>2 [[1,2],[2],[4]]=>2 [[1,2],[3],[4]]=>2 [[1,3],[2],[4]]=>2 [[1,4],[2],[3]]=>1 [[1,4],[2],[4]]=>2 [[1,3],[3],[4]]=>3 [[1,4],[3],[4]]=>3 [[2,2],[3],[4]]=>3 [[2,3],[3],[4]]=>4 [[2,4],[3],[4]]=>4 [[1],[2],[3],[4]]=>0 [[1,1,1,1,1]]=>0 [[1,1,1,1,2]]=>0 [[1,1,1,2,2]]=>0 [[1,1,2,2,2]]=>0 [[1,2,2,2,2]]=>0 [[2,2,2,2,2]]=>1 [[1,1,1,1],[2]]=>0 [[1,1,1,2],[2]]=>0 [[1,1,2,2],[2]]=>0 [[1,2,2,2],[2]]=>1 [[1,1,1],[2,2]]=>0 [[1,1,2],[2,2]]=>1 [[1,1,1,1,3]]=>0 [[1,1,1,2,3]]=>0 [[1,1,1,3,3]]=>0 [[1,1,2,2,3]]=>0 [[1,1,2,3,3]]=>0 [[1,1,3,3,3]]=>0 [[1,2,2,2,3]]=>0 [[1,2,2,3,3]]=>0 [[1,2,3,3,3]]=>0 [[1,3,3,3,3]]=>0 [[2,2,2,2,3]]=>1 [[2,2,2,3,3]]=>1 [[2,2,3,3,3]]=>1 [[2,3,3,3,3]]=>1 [[3,3,3,3,3]]=>1 [[1,1,1,1],[3]]=>1 [[1,1,1,2],[3]]=>1 [[1,1,1,3],[2]]=>0 [[1,1,1,3],[3]]=>1 [[1,1,2,2],[3]]=>1 [[1,1,2,3],[2]]=>0 [[1,1,2,3],[3]]=>1 [[1,1,3,3],[2]]=>0 [[1,1,3,3],[3]]=>1 [[1,2,2,2],[3]]=>1 [[1,2,2,3],[2]]=>1 [[1,2,2,3],[3]]=>1 [[1,2,3,3],[2]]=>1 [[1,2,3,3],[3]]=>1 [[1,3,3,3],[2]]=>1 [[1,3,3,3],[3]]=>2 [[2,2,2,2],[3]]=>2 [[2,2,2,3],[3]]=>2 [[2,2,3,3],[3]]=>2 [[2,3,3,3],[3]]=>3 [[1,1,1],[2,3]]=>0 [[1,1,1],[3,3]]=>1 [[1,1,2],[2,3]]=>0 [[1,1,3],[2,2]]=>1 [[1,1,2],[3,3]]=>1 [[1,1,3],[2,3]]=>1 [[1,1,3],[3,3]]=>2 [[1,2,2],[2,3]]=>1 [[1,2,2],[3,3]]=>1 [[1,2,3],[2,3]]=>2 [[1,2,3],[3,3]]=>2 [[2,2,2],[3,3]]=>2 [[2,2,3],[3,3]]=>3 [[1,1,1],[2],[3]]=>0 [[1,1,2],[2],[3]]=>0 [[1,1,3],[2],[3]]=>0 [[1,2,2],[2],[3]]=>1 [[1,2,3],[2],[3]]=>1 [[1,3,3],[2],[3]]=>1 [[1,1],[2,2],[3]]=>0 [[1,1],[2,3],[3]]=>1 [[1,2],[2,3],[3]]=>2 [[1,1,1,1,4]]=>0 [[1,1,1,2,4]]=>0 [[1,1,1,3,4]]=>0 [[1,1,1,4,4]]=>0 [[1,1,2,2,4]]=>0 [[1,1,2,3,4]]=>0 [[1,1,2,4,4]]=>0 [[1,1,3,3,4]]=>0 [[1,1,3,4,4]]=>0 [[1,1,4,4,4]]=>0 [[1,2,2,2,4]]=>0 [[1,2,2,3,4]]=>0 [[1,2,2,4,4]]=>0 [[1,2,3,3,4]]=>0 [[1,2,3,4,4]]=>0 [[1,2,4,4,4]]=>0 [[1,3,3,3,4]]=>0 [[1,3,3,4,4]]=>0 [[1,3,4,4,4]]=>0 [[1,4,4,4,4]]=>0 [[2,2,2,2,4]]=>1 [[2,2,2,3,4]]=>1 [[2,2,2,4,4]]=>1 [[2,2,3,3,4]]=>1 [[2,2,3,4,4]]=>1 [[2,2,4,4,4]]=>1 [[2,3,3,3,4]]=>1 [[2,3,3,4,4]]=>1 [[2,3,4,4,4]]=>1 [[2,4,4,4,4]]=>1 [[3,3,3,3,4]]=>1 [[3,3,3,4,4]]=>1 [[3,3,4,4,4]]=>1 [[3,4,4,4,4]]=>1 [[4,4,4,4,4]]=>1 [[1,1,1,1],[4]]=>1 [[1,1,1,2],[4]]=>1 [[1,1,1,4],[2]]=>0 [[1,1,1,3],[4]]=>1 [[1,1,1,4],[3]]=>1 [[1,1,1,4],[4]]=>1 [[1,1,2,2],[4]]=>1 [[1,1,2,4],[2]]=>0 [[1,1,2,3],[4]]=>1 [[1,1,2,4],[3]]=>1 [[1,1,3,4],[2]]=>0 [[1,1,2,4],[4]]=>1 [[1,1,4,4],[2]]=>0 [[1,1,3,3],[4]]=>1 [[1,1,3,4],[3]]=>1 [[1,1,3,4],[4]]=>1 [[1,1,4,4],[3]]=>1 [[1,1,4,4],[4]]=>1 [[1,2,2,2],[4]]=>1 [[1,2,2,4],[2]]=>1 [[1,2,2,3],[4]]=>1 [[1,2,2,4],[3]]=>1 [[1,2,3,4],[2]]=>1 [[1,2,2,4],[4]]=>1 [[1,2,4,4],[2]]=>1 [[1,2,3,3],[4]]=>1 [[1,2,3,4],[3]]=>1 [[1,3,3,4],[2]]=>1 [[1,2,3,4],[4]]=>1 [[1,2,4,4],[3]]=>1 [[1,3,4,4],[2]]=>1 [[1,2,4,4],[4]]=>1 [[1,4,4,4],[2]]=>1 [[1,3,3,3],[4]]=>1 [[1,3,3,4],[3]]=>2 [[1,3,3,4],[4]]=>1 [[1,3,4,4],[3]]=>2 [[1,3,4,4],[4]]=>1 [[1,4,4,4],[3]]=>2 [[1,4,4,4],[4]]=>2 [[2,2,2,2],[4]]=>2 [[2,2,2,3],[4]]=>2 [[2,2,2,4],[3]]=>2 [[2,2,2,4],[4]]=>2 [[2,2,3,3],[4]]=>2 [[2,2,3,4],[3]]=>2 [[2,2,3,4],[4]]=>2 [[2,2,4,4],[3]]=>2 [[2,2,4,4],[4]]=>2 [[2,3,3,3],[4]]=>2 [[2,3,3,4],[3]]=>3 [[2,3,3,4],[4]]=>2 [[2,3,4,4],[3]]=>3 [[2,3,4,4],[4]]=>2 [[2,4,4,4],[3]]=>3 [[2,4,4,4],[4]]=>3 [[3,3,3,3],[4]]=>2 [[3,3,3,4],[4]]=>2 [[3,3,4,4],[4]]=>2 [[3,4,4,4],[4]]=>3 [[1,1,1],[2,4]]=>0 [[1,1,1],[3,4]]=>1 [[1,1,1],[4,4]]=>1 [[1,1,2],[2,4]]=>0 [[1,1,4],[2,2]]=>1 [[1,1,2],[3,4]]=>1 [[1,1,3],[2,4]]=>0 [[1,1,4],[2,3]]=>1 [[1,1,2],[4,4]]=>1 [[1,1,4],[2,4]]=>1 [[1,1,3],[3,4]]=>1 [[1,1,4],[3,3]]=>2 [[1,1,3],[4,4]]=>1 [[1,1,4],[3,4]]=>2 [[1,1,4],[4,4]]=>2 [[1,2,2],[2,4]]=>1 [[1,2,2],[3,4]]=>2 [[1,2,3],[2,4]]=>1 [[1,2,4],[2,3]]=>2 [[1,2,2],[4,4]]=>1 [[1,2,4],[2,4]]=>2 [[1,2,3],[3,4]]=>2 [[1,2,4],[3,3]]=>2 [[1,3,3],[2,4]]=>1 [[1,2,3],[4,4]]=>1 [[1,2,4],[3,4]]=>3 [[1,3,4],[2,4]]=>2 [[1,2,4],[4,4]]=>2 [[1,3,3],[3,4]]=>2 [[1,3,3],[4,4]]=>1 [[1,3,4],[3,4]]=>3 [[1,3,4],[4,4]]=>2 [[2,2,2],[3,4]]=>2 [[2,2,2],[4,4]]=>2 [[2,2,3],[3,4]]=>2 [[2,2,4],[3,3]]=>3 [[2,2,3],[4,4]]=>2 [[2,2,4],[3,4]]=>3 [[2,2,4],[4,4]]=>3 [[2,3,3],[3,4]]=>3 [[2,3,3],[4,4]]=>2 [[2,3,4],[3,4]]=>4 [[2,3,4],[4,4]]=>3 [[3,3,3],[4,4]]=>2 [[3,3,4],[4,4]]=>3 [[1,1,1],[2],[4]]=>1 [[1,1,1],[3],[4]]=>2 [[1,1,2],[2],[4]]=>1 [[1,1,2],[3],[4]]=>2 [[1,1,3],[2],[4]]=>1 [[1,1,4],[2],[3]]=>0 [[1,1,4],[2],[4]]=>1 [[1,1,3],[3],[4]]=>2 [[1,1,4],[3],[4]]=>2 [[1,2,2],[2],[4]]=>2 [[1,2,2],[3],[4]]=>2 [[1,2,3],[2],[4]]=>2 [[1,2,4],[2],[3]]=>1 [[1,2,4],[2],[4]]=>2 [[1,2,3],[3],[4]]=>2 [[1,3,3],[2],[4]]=>2 [[1,3,4],[2],[3]]=>1 [[1,2,4],[3],[4]]=>2 [[1,3,4],[2],[4]]=>2 [[1,4,4],[2],[3]]=>1 [[1,4,4],[2],[4]]=>2 [[1,3,3],[3],[4]]=>3 [[1,3,4],[3],[4]]=>3 [[1,4,4],[3],[4]]=>3 [[2,2,2],[3],[4]]=>3 [[2,2,3],[3],[4]]=>3 [[2,2,4],[3],[4]]=>3 [[2,3,3],[3],[4]]=>4 [[2,3,4],[3],[4]]=>4 [[2,4,4],[3],[4]]=>4 [[1,1],[2,2],[4]]=>1 [[1,1],[2,3],[4]]=>1 [[1,1],[2,4],[3]]=>1 [[1,1],[2,4],[4]]=>2 [[1,1],[3,3],[4]]=>2 [[1,1],[3,4],[4]]=>3 [[1,2],[2,3],[4]]=>2 [[1,2],[2,4],[3]]=>2 [[1,2],[2,4],[4]]=>3 [[1,2],[3,3],[4]]=>2 [[1,3],[2,4],[3]]=>2 [[1,2],[3,4],[4]]=>4 [[1,3],[2,4],[4]]=>3 [[1,3],[3,4],[4]]=>4 [[2,2],[3,3],[4]]=>3 [[2,2],[3,4],[4]]=>4 [[2,3],[3,4],[4]]=>5 [[1,1],[2],[3],[4]]=>0 [[1,2],[2],[3],[4]]=>1 [[1,3],[2],[3],[4]]=>1 [[1,4],[2],[3],[4]]=>1 [[1,1,1,1,1,1]]=>0 [[1,1,1,1,1,2]]=>0 [[1,1,1,1,2,2]]=>0 [[1,1,1,2,2,2]]=>0 [[1,1,2,2,2,2]]=>0 [[1,2,2,2,2,2]]=>0 [[2,2,2,2,2,2]]=>1 [[1,1,1,1,1],[2]]=>0 [[1,1,1,1,2],[2]]=>0 [[1,1,1,2,2],[2]]=>0 [[1,1,2,2,2],[2]]=>0 [[1,2,2,2,2],[2]]=>1 [[1,1,1,1],[2,2]]=>0 [[1,1,1,2],[2,2]]=>0 [[1,1,2,2],[2,2]]=>1 [[1,1,1],[2,2,2]]=>0 [[1,1,1,1,1,3]]=>0 [[1,1,1,1,2,3]]=>0 [[1,1,1,1,3,3]]=>0 [[1,1,1,2,2,3]]=>0 [[1,1,1,2,3,3]]=>0 [[1,1,1,3,3,3]]=>0 [[1,1,2,2,2,3]]=>0 [[1,1,2,2,3,3]]=>0 [[1,1,2,3,3,3]]=>0 [[1,1,3,3,3,3]]=>0 [[1,2,2,2,2,3]]=>0 [[1,2,2,2,3,3]]=>0 [[1,2,2,3,3,3]]=>0 [[1,2,3,3,3,3]]=>0 [[1,3,3,3,3,3]]=>0 [[2,2,2,2,2,3]]=>1 [[2,2,2,2,3,3]]=>1 [[2,2,2,3,3,3]]=>1 [[2,2,3,3,3,3]]=>1 [[2,3,3,3,3,3]]=>1 [[3,3,3,3,3,3]]=>1 [[1,1,1,1,1],[3]]=>1 [[1,1,1,1,2],[3]]=>1 [[1,1,1,1,3],[2]]=>0 [[1,1,1,1,3],[3]]=>1 [[1,1,1,2,2],[3]]=>1 [[1,1,1,2,3],[2]]=>0 [[1,1,1,2,3],[3]]=>1 [[1,1,1,3,3],[2]]=>0 [[1,1,1,3,3],[3]]=>1 [[1,1,2,2,2],[3]]=>1 [[1,1,2,2,3],[2]]=>0 [[1,1,2,2,3],[3]]=>1 [[1,1,2,3,3],[2]]=>0 [[1,1,2,3,3],[3]]=>1 [[1,1,3,3,3],[2]]=>0 [[1,1,3,3,3],[3]]=>1 [[1,2,2,2,2],[3]]=>1 [[1,2,2,2,3],[2]]=>1 [[1,2,2,2,3],[3]]=>1 [[1,2,2,3,3],[2]]=>1 [[1,2,2,3,3],[3]]=>1 [[1,2,3,3,3],[2]]=>1 [[1,2,3,3,3],[3]]=>1 [[1,3,3,3,3],[2]]=>1 [[1,3,3,3,3],[3]]=>2 [[2,2,2,2,2],[3]]=>2 [[2,2,2,2,3],[3]]=>2 [[2,2,2,3,3],[3]]=>2 [[2,2,3,3,3],[3]]=>2 [[2,3,3,3,3],[3]]=>3 [[1,1,1,1],[2,3]]=>0 [[1,1,1,1],[3,3]]=>1 [[1,1,1,2],[2,3]]=>0 [[1,1,1,3],[2,2]]=>0 [[1,1,1,2],[3,3]]=>1 [[1,1,1,3],[2,3]]=>0 [[1,1,1,3],[3,3]]=>1 [[1,1,2,2],[2,3]]=>0 [[1,1,2,3],[2,2]]=>1 [[1,1,2,2],[3,3]]=>1 [[1,1,2,3],[2,3]]=>0 [[1,1,3,3],[2,2]]=>1 [[1,1,2,3],[3,3]]=>1 [[1,1,3,3],[2,3]]=>1 [[1,1,3,3],[3,3]]=>2 [[1,2,2,2],[2,3]]=>1 [[1,2,2,2],[3,3]]=>1 [[1,2,2,3],[2,3]]=>1 [[1,2,2,3],[3,3]]=>1 [[1,2,3,3],[2,3]]=>2 [[1,2,3,3],[3,3]]=>2 [[2,2,2,2],[3,3]]=>2 [[2,2,2,3],[3,3]]=>2 [[2,2,3,3],[3,3]]=>3 [[1,1,1,1],[2],[3]]=>0 [[1,1,1,2],[2],[3]]=>0 [[1,1,1,3],[2],[3]]=>0 [[1,1,2,2],[2],[3]]=>0 [[1,1,2,3],[2],[3]]=>0 [[1,1,3,3],[2],[3]]=>0 [[1,2,2,2],[2],[3]]=>1 [[1,2,2,3],[2],[3]]=>1 [[1,2,3,3],[2],[3]]=>1 [[1,3,3,3],[2],[3]]=>1 [[1,1,1],[2,2,3]]=>0 [[1,1,1],[2,3,3]]=>0 [[1,1,1],[3,3,3]]=>1 [[1,1,2],[2,2,3]]=>1 [[1,1,2],[2,3,3]]=>0 [[1,1,2],[3,3,3]]=>1 [[1,2,2],[2,3,3]]=>1 [[1,2,2],[3,3,3]]=>1 [[2,2,2],[3,3,3]]=>2 [[1,1,1],[2,2],[3]]=>0 [[1,1,1],[2,3],[3]]=>1 [[1,1,2],[2,2],[3]]=>1 [[1,1,2],[2,3],[3]]=>1 [[1,1,3],[2,2],[3]]=>1 [[1,1,3],[2,3],[3]]=>2 [[1,2,2],[2,3],[3]]=>2 [[1,2,3],[2,3],[3]]=>3 [[1,1],[2,2],[3,3]]=>0 [[1,1,1,1,1,4]]=>0 [[1,1,1,1,2,4]]=>0 [[1,1,1,1,3,4]]=>0 [[1,1,1,1,4,4]]=>0 [[1,1,1,2,2,4]]=>0 [[1,1,1,2,3,4]]=>0 [[1,1,1,2,4,4]]=>0 [[1,1,1,3,3,4]]=>0 [[1,1,1,3,4,4]]=>0 [[1,1,1,4,4,4]]=>0 [[1,1,2,2,2,4]]=>0 [[1,1,2,2,3,4]]=>0 [[1,1,2,2,4,4]]=>0 [[1,1,2,3,3,4]]=>0 [[1,1,2,3,4,4]]=>0 [[1,1,2,4,4,4]]=>0 [[1,1,3,3,3,4]]=>0 [[1,1,3,3,4,4]]=>0 [[1,1,3,4,4,4]]=>0 [[1,1,4,4,4,4]]=>0 [[1,2,2,2,2,4]]=>0 [[1,2,2,2,3,4]]=>0 [[1,2,2,2,4,4]]=>0 [[1,2,2,3,3,4]]=>0 [[1,2,2,3,4,4]]=>0 [[1,2,2,4,4,4]]=>0 [[1,2,3,3,3,4]]=>0 [[1,2,3,3,4,4]]=>0 [[1,2,3,4,4,4]]=>0 [[1,2,4,4,4,4]]=>0 [[1,3,3,3,3,4]]=>0 [[1,3,3,3,4,4]]=>0 [[1,3,3,4,4,4]]=>0 [[1,3,4,4,4,4]]=>0 [[1,4,4,4,4,4]]=>0 [[2,2,2,2,2,4]]=>1 [[2,2,2,2,3,4]]=>1 [[2,2,2,2,4,4]]=>1 [[2,2,2,3,3,4]]=>1 [[2,2,2,3,4,4]]=>1 [[2,2,2,4,4,4]]=>1 [[2,2,3,3,3,4]]=>1 [[2,2,3,3,4,4]]=>1 [[2,2,3,4,4,4]]=>1 [[2,2,4,4,4,4]]=>1 [[2,3,3,3,3,4]]=>1 [[2,3,3,3,4,4]]=>1 [[2,3,3,4,4,4]]=>1 [[2,3,4,4,4,4]]=>1 [[2,4,4,4,4,4]]=>1 [[3,3,3,3,3,4]]=>1 [[3,3,3,3,4,4]]=>1 [[3,3,3,4,4,4]]=>1 [[3,3,4,4,4,4]]=>1 [[3,4,4,4,4,4]]=>1 [[4,4,4,4,4,4]]=>1 [[1,1,1,1,1],[4]]=>1 [[1,1,1,1,2],[4]]=>1 [[1,1,1,1,4],[2]]=>0 [[1,1,1,1,3],[4]]=>1 [[1,1,1,1,4],[3]]=>1 [[1,1,1,1,4],[4]]=>1 [[1,1,1,2,2],[4]]=>1 [[1,1,1,2,4],[2]]=>0 [[1,1,1,2,3],[4]]=>1 [[1,1,1,2,4],[3]]=>1 [[1,1,1,3,4],[2]]=>0 [[1,1,1,2,4],[4]]=>1 [[1,1,1,4,4],[2]]=>0 [[1,1,1,3,3],[4]]=>1 [[1,1,1,3,4],[3]]=>1 [[1,1,1,3,4],[4]]=>1 [[1,1,1,4,4],[3]]=>1 [[1,1,1,4,4],[4]]=>1 [[1,1,2,2,2],[4]]=>1 [[1,1,2,2,4],[2]]=>0 [[1,1,2,2,3],[4]]=>1 [[1,1,2,2,4],[3]]=>1 [[1,1,2,3,4],[2]]=>0 [[1,1,2,2,4],[4]]=>1 [[1,1,2,4,4],[2]]=>0 [[1,1,2,3,3],[4]]=>1 [[1,1,2,3,4],[3]]=>1 [[1,1,3,3,4],[2]]=>0 [[1,1,2,3,4],[4]]=>1 [[1,1,2,4,4],[3]]=>1 [[1,1,3,4,4],[2]]=>0 [[1,1,2,4,4],[4]]=>1 [[1,1,4,4,4],[2]]=>0 [[1,1,3,3,3],[4]]=>1 [[1,1,3,3,4],[3]]=>1 [[1,1,3,3,4],[4]]=>1 [[1,1,3,4,4],[3]]=>1 [[1,1,3,4,4],[4]]=>1 [[1,1,4,4,4],[3]]=>1 [[1,1,4,4,4],[4]]=>1 [[1,2,2,2,2],[4]]=>1 [[1,2,2,2,4],[2]]=>1 [[1,2,2,2,3],[4]]=>1 [[1,2,2,2,4],[3]]=>1 [[1,2,2,3,4],[2]]=>1 [[1,2,2,2,4],[4]]=>1 [[1,2,2,4,4],[2]]=>1 [[1,2,2,3,3],[4]]=>1 [[1,2,2,3,4],[3]]=>1 [[1,2,3,3,4],[2]]=>1 [[1,2,2,3,4],[4]]=>1 [[1,2,2,4,4],[3]]=>1 [[1,2,3,4,4],[2]]=>1 [[1,2,2,4,4],[4]]=>1 [[1,2,4,4,4],[2]]=>1 [[1,2,3,3,3],[4]]=>1 [[1,2,3,3,4],[3]]=>1 [[1,3,3,3,4],[2]]=>1 [[1,2,3,3,4],[4]]=>1 [[1,2,3,4,4],[3]]=>1 [[1,3,3,4,4],[2]]=>1 [[1,2,3,4,4],[4]]=>1 [[1,2,4,4,4],[3]]=>1 [[1,3,4,4,4],[2]]=>1 [[1,2,4,4,4],[4]]=>1 [[1,4,4,4,4],[2]]=>1 [[1,3,3,3,3],[4]]=>1 [[1,3,3,3,4],[3]]=>2 [[1,3,3,3,4],[4]]=>1 [[1,3,3,4,4],[3]]=>2 [[1,3,3,4,4],[4]]=>1 [[1,3,4,4,4],[3]]=>2 [[1,3,4,4,4],[4]]=>1 [[1,4,4,4,4],[3]]=>2 [[1,4,4,4,4],[4]]=>2 [[2,2,2,2,2],[4]]=>2 [[2,2,2,2,3],[4]]=>2 [[2,2,2,2,4],[3]]=>2 [[2,2,2,2,4],[4]]=>2 [[2,2,2,3,3],[4]]=>2 [[2,2,2,3,4],[3]]=>2 [[2,2,2,3,4],[4]]=>2 [[2,2,2,4,4],[3]]=>2 [[2,2,2,4,4],[4]]=>2 [[2,2,3,3,3],[4]]=>2 [[2,2,3,3,4],[3]]=>2 [[2,2,3,3,4],[4]]=>2 [[2,2,3,4,4],[3]]=>2 [[2,2,3,4,4],[4]]=>2 [[2,2,4,4,4],[3]]=>2 [[2,2,4,4,4],[4]]=>2 [[2,3,3,3,3],[4]]=>2 [[2,3,3,3,4],[3]]=>3 [[2,3,3,3,4],[4]]=>2 [[2,3,3,4,4],[3]]=>3 [[2,3,3,4,4],[4]]=>2 [[2,3,4,4,4],[3]]=>3 [[2,3,4,4,4],[4]]=>2 [[2,4,4,4,4],[3]]=>3 [[2,4,4,4,4],[4]]=>3 [[3,3,3,3,3],[4]]=>2 [[3,3,3,3,4],[4]]=>2 [[3,3,3,4,4],[4]]=>2 [[3,3,4,4,4],[4]]=>2 [[3,4,4,4,4],[4]]=>3 [[1,1,1,1],[2,4]]=>0 [[1,1,1,1],[3,4]]=>1 [[1,1,1,1],[4,4]]=>1 [[1,1,1,2],[2,4]]=>0 [[1,1,1,4],[2,2]]=>0 [[1,1,1,2],[3,4]]=>1 [[1,1,1,3],[2,4]]=>0 [[1,1,1,4],[2,3]]=>0 [[1,1,1,2],[4,4]]=>1 [[1,1,1,4],[2,4]]=>0 [[1,1,1,3],[3,4]]=>1 [[1,1,1,4],[3,3]]=>1 [[1,1,1,3],[4,4]]=>1 [[1,1,1,4],[3,4]]=>1 [[1,1,1,4],[4,4]]=>1 [[1,1,2,2],[2,4]]=>0 [[1,1,2,4],[2,2]]=>1 [[1,1,2,2],[3,4]]=>1 [[1,1,2,3],[2,4]]=>0 [[1,1,2,4],[2,3]]=>0 [[1,1,3,4],[2,2]]=>1 [[1,1,2,2],[4,4]]=>1 [[1,1,2,4],[2,4]]=>0 [[1,1,4,4],[2,2]]=>1 [[1,1,2,3],[3,4]]=>1 [[1,1,2,4],[3,3]]=>1 [[1,1,3,3],[2,4]]=>0 [[1,1,3,4],[2,3]]=>1 [[1,1,2,3],[4,4]]=>1 [[1,1,2,4],[3,4]]=>1 [[1,1,3,4],[2,4]]=>0 [[1,1,4,4],[2,3]]=>1 [[1,1,2,4],[4,4]]=>1 [[1,1,4,4],[2,4]]=>1 [[1,1,3,3],[3,4]]=>1 [[1,1,3,4],[3,3]]=>2 [[1,1,3,3],[4,4]]=>1 [[1,1,3,4],[3,4]]=>1 [[1,1,4,4],[3,3]]=>2 [[1,1,3,4],[4,4]]=>1 [[1,1,4,4],[3,4]]=>2 [[1,1,4,4],[4,4]]=>2 [[1,2,2,2],[2,4]]=>1 [[1,2,2,2],[3,4]]=>2 [[1,2,2,3],[2,4]]=>1 [[1,2,2,4],[2,3]]=>1 [[1,2,2,2],[4,4]]=>1 [[1,2,2,4],[2,4]]=>1 [[1,2,2,3],[3,4]]=>2 [[1,2,2,4],[3,3]]=>1 [[1,2,3,3],[2,4]]=>1 [[1,2,3,4],[2,3]]=>2 [[1,2,2,3],[4,4]]=>1 [[1,2,2,4],[3,4]]=>2 [[1,2,3,4],[2,4]]=>1 [[1,2,4,4],[2,3]]=>2 [[1,2,2,4],[4,4]]=>1 [[1,2,4,4],[2,4]]=>2 [[1,2,3,3],[3,4]]=>2 [[1,2,3,4],[3,3]]=>2 [[1,3,3,3],[2,4]]=>1 [[1,2,3,3],[4,4]]=>1 [[1,2,3,4],[3,4]]=>2 [[1,2,4,4],[3,3]]=>2 [[1,3,3,4],[2,4]]=>1 [[1,2,3,4],[4,4]]=>1 [[1,2,4,4],[3,4]]=>3 [[1,3,4,4],[2,4]]=>2 [[1,2,4,4],[4,4]]=>2 [[1,3,3,3],[3,4]]=>2 [[1,3,3,3],[4,4]]=>1 [[1,3,3,4],[3,4]]=>2 [[1,3,3,4],[4,4]]=>1 [[1,3,4,4],[3,4]]=>3 [[1,3,4,4],[4,4]]=>2 [[2,2,2,2],[3,4]]=>2 [[2,2,2,2],[4,4]]=>2 [[2,2,2,3],[3,4]]=>2 [[2,2,2,4],[3,3]]=>2 [[2,2,2,3],[4,4]]=>2 [[2,2,2,4],[3,4]]=>2 [[2,2,2,4],[4,4]]=>2 [[2,2,3,3],[3,4]]=>2 [[2,2,3,4],[3,3]]=>3 [[2,2,3,3],[4,4]]=>2 [[2,2,3,4],[3,4]]=>2 [[2,2,4,4],[3,3]]=>3 [[2,2,3,4],[4,4]]=>2 [[2,2,4,4],[3,4]]=>3 [[2,2,4,4],[4,4]]=>3 [[2,3,3,3],[3,4]]=>3 [[2,3,3,3],[4,4]]=>2 [[2,3,3,4],[3,4]]=>3 [[2,3,3,4],[4,4]]=>2 [[2,3,4,4],[3,4]]=>4 [[2,3,4,4],[4,4]]=>3 [[3,3,3,3],[4,4]]=>2 [[3,3,3,4],[4,4]]=>2 [[3,3,4,4],[4,4]]=>3 [[1,1,1,1],[2],[4]]=>1 [[1,1,1,1],[3],[4]]=>2 [[1,1,1,2],[2],[4]]=>1 [[1,1,1,2],[3],[4]]=>2 [[1,1,1,3],[2],[4]]=>1 [[1,1,1,4],[2],[3]]=>0 [[1,1,1,4],[2],[4]]=>1 [[1,1,1,3],[3],[4]]=>2 [[1,1,1,4],[3],[4]]=>2 [[1,1,2,2],[2],[4]]=>1 [[1,1,2,2],[3],[4]]=>2 [[1,1,2,3],[2],[4]]=>1 [[1,1,2,4],[2],[3]]=>0 [[1,1,2,4],[2],[4]]=>1 [[1,1,2,3],[3],[4]]=>2 [[1,1,3,3],[2],[4]]=>1 [[1,1,3,4],[2],[3]]=>0 [[1,1,2,4],[3],[4]]=>2 [[1,1,3,4],[2],[4]]=>1 [[1,1,4,4],[2],[3]]=>0 [[1,1,4,4],[2],[4]]=>1 [[1,1,3,3],[3],[4]]=>2 [[1,1,3,4],[3],[4]]=>2 [[1,1,4,4],[3],[4]]=>2 [[1,2,2,2],[2],[4]]=>2 [[1,2,2,2],[3],[4]]=>2 [[1,2,2,3],[2],[4]]=>2 [[1,2,2,4],[2],[3]]=>1 [[1,2,2,4],[2],[4]]=>2 [[1,2,2,3],[3],[4]]=>2 [[1,2,3,3],[2],[4]]=>2 [[1,2,3,4],[2],[3]]=>1 [[1,2,2,4],[3],[4]]=>2 [[1,2,3,4],[2],[4]]=>2 [[1,2,4,4],[2],[3]]=>1 [[1,2,4,4],[2],[4]]=>2 [[1,2,3,3],[3],[4]]=>2 [[1,3,3,3],[2],[4]]=>2 [[1,3,3,4],[2],[3]]=>1 [[1,2,3,4],[3],[4]]=>2 [[1,3,3,4],[2],[4]]=>2 [[1,3,4,4],[2],[3]]=>1 [[1,2,4,4],[3],[4]]=>2 [[1,3,4,4],[2],[4]]=>2 [[1,4,4,4],[2],[3]]=>1 [[1,4,4,4],[2],[4]]=>2 [[1,3,3,3],[3],[4]]=>3 [[1,3,3,4],[3],[4]]=>3 [[1,3,4,4],[3],[4]]=>3 [[1,4,4,4],[3],[4]]=>3 [[2,2,2,2],[3],[4]]=>3 [[2,2,2,3],[3],[4]]=>3 [[2,2,2,4],[3],[4]]=>3 [[2,2,3,3],[3],[4]]=>3 [[2,2,3,4],[3],[4]]=>3 [[2,2,4,4],[3],[4]]=>3 [[2,3,3,3],[3],[4]]=>4 [[2,3,3,4],[3],[4]]=>4 [[2,3,4,4],[3],[4]]=>4 [[2,4,4,4],[3],[4]]=>4 [[1,1,1],[2,2,4]]=>0 [[1,1,1],[2,3,4]]=>0 [[1,1,1],[2,4,4]]=>0 [[1,1,1],[3,3,4]]=>1 [[1,1,1],[3,4,4]]=>1 [[1,1,1],[4,4,4]]=>1 [[1,1,2],[2,2,4]]=>1 [[1,1,2],[2,3,4]]=>1 [[1,1,3],[2,2,4]]=>1 [[1,1,2],[2,4,4]]=>0 [[1,1,2],[3,3,4]]=>2 [[1,1,3],[2,3,4]]=>1 [[1,1,2],[3,4,4]]=>1 [[1,1,3],[2,4,4]]=>0 [[1,1,2],[4,4,4]]=>1 [[1,1,3],[3,3,4]]=>2 [[1,1,3],[3,4,4]]=>1 [[1,1,3],[4,4,4]]=>1 [[1,2,2],[2,3,4]]=>1 [[1,2,2],[2,4,4]]=>1 [[1,2,2],[3,3,4]]=>1 [[1,2,3],[2,3,4]]=>2 [[1,2,2],[3,4,4]]=>2 [[1,2,3],[2,4,4]]=>1 [[1,2,2],[4,4,4]]=>1 [[1,2,3],[3,3,4]]=>2 [[1,2,3],[3,4,4]]=>2 [[1,3,3],[2,4,4]]=>1 [[1,2,3],[4,4,4]]=>1 [[1,3,3],[3,4,4]]=>2 [[1,3,3],[4,4,4]]=>1 [[2,2,2],[3,3,4]]=>2 [[2,2,2],[3,4,4]]=>2 [[2,2,2],[4,4,4]]=>2 [[2,2,3],[3,3,4]]=>3 [[2,2,3],[3,4,4]]=>2 [[2,2,3],[4,4,4]]=>2 [[2,3,3],[3,4,4]]=>3 [[2,3,3],[4,4,4]]=>2 [[3,3,3],[4,4,4]]=>2 [[1,1,1],[2,2],[4]]=>1 [[1,1,1],[2,3],[4]]=>1 [[1,1,1],[2,4],[3]]=>1 [[1,1,1],[2,4],[4]]=>2 [[1,1,1],[3,3],[4]]=>2 [[1,1,1],[3,4],[4]]=>3 [[1,1,2],[2,2],[4]]=>2 [[1,1,2],[2,3],[4]]=>1 [[1,1,2],[2,4],[3]]=>1 [[1,1,3],[2,2],[4]]=>2 [[1,1,4],[2,2],[3]]=>1 [[1,1,2],[2,4],[4]]=>2 [[1,1,4],[2,2],[4]]=>2 [[1,1,2],[3,3],[4]]=>2 [[1,1,3],[2,3],[4]]=>2 [[1,1,3],[2,4],[3]]=>1 [[1,1,4],[2,3],[3]]=>2 [[1,1,2],[3,4],[4]]=>3 [[1,1,3],[2,4],[4]]=>2 [[1,1,4],[2,3],[4]]=>2 [[1,1,4],[2,4],[3]]=>2 [[1,1,4],[2,4],[4]]=>3 [[1,1,3],[3,3],[4]]=>3 [[1,1,3],[3,4],[4]]=>3 [[1,1,4],[3,3],[4]]=>3 [[1,1,4],[3,4],[4]]=>4 [[1,2,2],[2,3],[4]]=>2 [[1,2,2],[2,4],[3]]=>2 [[1,2,2],[2,4],[4]]=>3 [[1,2,2],[3,3],[4]]=>2 [[1,2,3],[2,3],[4]]=>3 [[1,2,3],[2,4],[3]]=>2 [[1,2,4],[2,3],[3]]=>3 [[1,2,2],[3,4],[4]]=>4 [[1,2,3],[2,4],[4]]=>3 [[1,2,4],[2,3],[4]]=>3 [[1,2,4],[2,4],[3]]=>3 [[1,2,4],[2,4],[4]]=>4 [[1,2,3],[3,3],[4]]=>3 [[1,3,3],[2,4],[3]]=>2 [[1,2,3],[3,4],[4]]=>4 [[1,2,4],[3,3],[4]]=>3 [[1,3,3],[2,4],[4]]=>3 [[1,3,4],[2,4],[3]]=>3 [[1,2,4],[3,4],[4]]=>5 [[1,3,4],[2,4],[4]]=>4 [[1,3,3],[3,4],[4]]=>4 [[1,3,4],[3,4],[4]]=>5 [[2,2,2],[3,3],[4]]=>3 [[2,2,2],[3,4],[4]]=>4 [[2,2,3],[3,3],[4]]=>4 [[2,2,3],[3,4],[4]]=>4 [[2,2,4],[3,3],[4]]=>4 [[2,2,4],[3,4],[4]]=>5 [[2,3,3],[3,4],[4]]=>5 [[2,3,4],[3,4],[4]]=>6 [[1,1,1],[2],[3],[4]]=>0 [[1,1,2],[2],[3],[4]]=>0 [[1,1,3],[2],[3],[4]]=>0 [[1,1,4],[2],[3],[4]]=>0 [[1,2,2],[2],[3],[4]]=>1 [[1,2,3],[2],[3],[4]]=>1 [[1,2,4],[2],[3],[4]]=>1 [[1,3,3],[2],[3],[4]]=>1 [[1,3,4],[2],[3],[4]]=>1 [[1,4,4],[2],[3],[4]]=>1 [[1,1],[2,2],[3,4]]=>0 [[1,1],[2,2],[4,4]]=>1 [[1,1],[2,3],[3,4]]=>1 [[1,1],[2,3],[4,4]]=>1 [[1,1],[3,3],[4,4]]=>2 [[1,2],[2,3],[3,4]]=>2 [[1,2],[2,3],[4,4]]=>2 [[1,2],[3,3],[4,4]]=>2 [[2,2],[3,3],[4,4]]=>3 [[1,1],[2,2],[3],[4]]=>0 [[1,1],[2,3],[3],[4]]=>1 [[1,1],[2,4],[3],[4]]=>1 [[1,2],[2,3],[3],[4]]=>2 [[1,2],[2,4],[3],[4]]=>2 [[1,3],[2,4],[3],[4]]=>2
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The flush statistic of a semistandard tableau.
Let $T$ be a tableaux with $r$ rows such that each row is longer than the row beneath it by at least one box. Let $1 \leq i < k \leq r+1$ and suppose $l$ is the smallest integer greater than $k$ such that there exists an $l$-segment in the $(i+1)$-st row of $T$. A $k$-segment in the $i$-th row of $T$ is called flush if the leftmost box in the $k$-segment and the leftmost box of the $l$-segment are in the same column of $T$. If, however, no such $l$ exists, then this $k$-segment is said to be flush if the number of boxes in the $k$-segment is equal to difference of the number of boxes between the $i$-th row and $(i+1)$-st row. The flush statistic is given by the number of $k$-segments in $T$.
References
[1] Salisbury, B. The flush statistic on semistandard Young tableaux arXiv:1401.1185
Code
def statistic(T):
    f = 0
    segments = {}
    for r in range(len(T)):
        for c in range(len(T[r])):
            for j in range(c+1):
                if T[r][j] != r+1:
                    if (r,T[r][j]) not in segments.keys():
                        segments[(r,T[r][j])] = j
    L = segments.items()
    for s in segments.iteritems():
        if s[0][0] != len(T)-1 and s[1] == len(T[s[0][0]+1]) and T[s[0][0]+1][-1] <= s[0][1]:
            f += 1
        if s[0][0] == len(T)-1 and s[1] == 0:
            f += 1
        else:
            for t in L:
                if s[0][0]+1 == t[0][0] and s[1] == t[1]:
                    if s[1] >= 1 and T[s[0][0]+1][s[1]] != T[s[0][0]+1][s[1]-1]:
                        f += 1
                    if s[1] < 1 and T[s[0][0]+1][s[1]] != s[0][0]+2:
                        f += 1
    return f
Created
Jan 15, 2014 at 19:13 by Ben Salisbury
Updated
Oct 19, 2015 at 16:34 by Christian Stump