Identifier
Values
=>
[1]=>[1]=>0 [1,1]=>[1,1]=>0 [1,2]=>[2,1]=>1 [2,1]=>[1,2]=>0 [1,1,1]=>[1,1,1]=>0 [1,1,2]=>[2,1,1]=>1 [1,2,1]=>[1,2,1]=>1 [2,1,1]=>[1,1,2]=>0 [1,1,3]=>[3,1,1]=>1 [1,3,1]=>[1,3,1]=>1 [3,1,1]=>[1,1,3]=>0 [1,2,2]=>[2,2,1]=>1 [2,1,2]=>[2,1,2]=>1 [2,2,1]=>[1,2,2]=>0 [1,2,3]=>[3,2,1]=>2 [1,3,2]=>[2,3,1]=>1 [2,1,3]=>[3,1,2]=>1 [2,3,1]=>[1,3,2]=>1 [3,1,2]=>[2,1,3]=>1 [3,2,1]=>[1,2,3]=>0 [1,1,1,1]=>[1,1,1,1]=>0 [1,1,1,2]=>[2,1,1,1]=>1 [1,1,2,1]=>[1,2,1,1]=>1 [1,2,1,1]=>[1,1,2,1]=>1 [2,1,1,1]=>[1,1,1,2]=>0 [1,1,1,3]=>[3,1,1,1]=>1 [1,1,3,1]=>[1,3,1,1]=>1 [1,3,1,1]=>[1,1,3,1]=>1 [3,1,1,1]=>[1,1,1,3]=>0 [1,1,1,4]=>[4,1,1,1]=>1 [1,1,4,1]=>[1,4,1,1]=>1 [1,4,1,1]=>[1,1,4,1]=>1 [4,1,1,1]=>[1,1,1,4]=>0 [1,1,2,2]=>[2,2,1,1]=>1 [1,2,1,2]=>[2,1,2,1]=>2 [1,2,2,1]=>[1,2,2,1]=>1 [2,1,1,2]=>[2,1,1,2]=>1 [2,1,2,1]=>[1,2,1,2]=>1 [2,2,1,1]=>[1,1,2,2]=>0 [1,1,2,3]=>[3,2,1,1]=>2 [1,1,3,2]=>[2,3,1,1]=>1 [1,2,1,3]=>[3,1,2,1]=>2 [1,2,3,1]=>[1,3,2,1]=>2 [1,3,1,2]=>[2,1,3,1]=>2 [1,3,2,1]=>[1,2,3,1]=>1 [2,1,1,3]=>[3,1,1,2]=>1 [2,1,3,1]=>[1,3,1,2]=>1 [2,3,1,1]=>[1,1,3,2]=>1 [3,1,1,2]=>[2,1,1,3]=>1 [3,1,2,1]=>[1,2,1,3]=>1 [3,2,1,1]=>[1,1,2,3]=>0 [1,1,2,4]=>[4,2,1,1]=>2 [1,1,4,2]=>[2,4,1,1]=>1 [1,2,1,4]=>[4,1,2,1]=>2 [1,2,4,1]=>[1,4,2,1]=>2 [1,4,1,2]=>[2,1,4,1]=>2 [1,4,2,1]=>[1,2,4,1]=>1 [2,1,1,4]=>[4,1,1,2]=>1 [2,1,4,1]=>[1,4,1,2]=>1 [2,4,1,1]=>[1,1,4,2]=>1 [4,1,1,2]=>[2,1,1,4]=>1 [4,1,2,1]=>[1,2,1,4]=>1 [4,2,1,1]=>[1,1,2,4]=>0 [1,1,3,3]=>[3,3,1,1]=>1 [1,3,1,3]=>[3,1,3,1]=>2 [1,3,3,1]=>[1,3,3,1]=>1 [3,1,1,3]=>[3,1,1,3]=>1 [3,1,3,1]=>[1,3,1,3]=>1 [3,3,1,1]=>[1,1,3,3]=>0 [1,1,3,4]=>[4,3,1,1]=>2 [1,1,4,3]=>[3,4,1,1]=>1 [1,3,1,4]=>[4,1,3,1]=>2 [1,3,4,1]=>[1,4,3,1]=>2 [1,4,1,3]=>[3,1,4,1]=>2 [1,4,3,1]=>[1,3,4,1]=>1 [3,1,1,4]=>[4,1,1,3]=>1 [3,1,4,1]=>[1,4,1,3]=>1 [3,4,1,1]=>[1,1,4,3]=>1 [4,1,1,3]=>[3,1,1,4]=>1 [4,1,3,1]=>[1,3,1,4]=>1 [4,3,1,1]=>[1,1,3,4]=>0 [1,2,2,2]=>[2,2,2,1]=>1 [2,1,2,2]=>[2,2,1,2]=>1 [2,2,1,2]=>[2,1,2,2]=>1 [2,2,2,1]=>[1,2,2,2]=>0 [1,2,2,3]=>[3,2,2,1]=>2 [1,2,3,2]=>[2,3,2,1]=>2 [1,3,2,2]=>[2,2,3,1]=>1 [2,1,2,3]=>[3,2,1,2]=>2 [2,1,3,2]=>[2,3,1,2]=>1 [2,2,1,3]=>[3,1,2,2]=>1 [2,2,3,1]=>[1,3,2,2]=>1 [2,3,1,2]=>[2,1,3,2]=>2 [2,3,2,1]=>[1,2,3,2]=>1 [3,1,2,2]=>[2,2,1,3]=>1 [3,2,1,2]=>[2,1,2,3]=>1 [3,2,2,1]=>[1,2,2,3]=>0 [1,2,2,4]=>[4,2,2,1]=>2 [1,2,4,2]=>[2,4,2,1]=>2 [1,4,2,2]=>[2,2,4,1]=>1 [2,1,2,4]=>[4,2,1,2]=>2 [2,1,4,2]=>[2,4,1,2]=>1 [2,2,1,4]=>[4,1,2,2]=>1 [2,2,4,1]=>[1,4,2,2]=>1 [2,4,1,2]=>[2,1,4,2]=>2 [2,4,2,1]=>[1,2,4,2]=>1 [4,1,2,2]=>[2,2,1,4]=>1 [4,2,1,2]=>[2,1,2,4]=>1 [4,2,2,1]=>[1,2,2,4]=>0 [1,2,3,3]=>[3,3,2,1]=>2 [1,3,2,3]=>[3,2,3,1]=>2 [1,3,3,2]=>[2,3,3,1]=>1 [2,1,3,3]=>[3,3,1,2]=>1 [2,3,1,3]=>[3,1,3,2]=>2 [2,3,3,1]=>[1,3,3,2]=>1 [3,1,2,3]=>[3,2,1,3]=>2 [3,1,3,2]=>[2,3,1,3]=>1 [3,2,1,3]=>[3,1,2,3]=>1 [3,2,3,1]=>[1,3,2,3]=>1 [3,3,1,2]=>[2,1,3,3]=>1 [3,3,2,1]=>[1,2,3,3]=>0 [1,2,3,4]=>[4,3,2,1]=>3 [1,2,4,3]=>[3,4,2,1]=>2 [1,3,2,4]=>[4,2,3,1]=>2 [1,3,4,2]=>[2,4,3,1]=>2 [1,4,2,3]=>[3,2,4,1]=>2 [1,4,3,2]=>[2,3,4,1]=>1 [2,1,3,4]=>[4,3,1,2]=>2 [2,1,4,3]=>[3,4,1,2]=>1 [2,3,1,4]=>[4,1,3,2]=>2 [2,3,4,1]=>[1,4,3,2]=>2 [2,4,1,3]=>[3,1,4,2]=>2 [2,4,3,1]=>[1,3,4,2]=>1 [3,1,2,4]=>[4,2,1,3]=>2 [3,1,4,2]=>[2,4,1,3]=>1 [3,2,1,4]=>[4,1,2,3]=>1 [3,2,4,1]=>[1,4,2,3]=>1 [3,4,1,2]=>[2,1,4,3]=>2 [3,4,2,1]=>[1,2,4,3]=>1 [4,1,2,3]=>[3,2,1,4]=>2 [4,1,3,2]=>[2,3,1,4]=>1 [4,2,1,3]=>[3,1,2,4]=>1 [4,2,3,1]=>[1,3,2,4]=>1 [4,3,1,2]=>[2,1,3,4]=>1 [4,3,2,1]=>[1,2,3,4]=>0
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Description
The number of descents in a parking function.
This is the number of indices $i$ such that $p_i > p_{i+1}$.
Map
reverse
Description
Return the reversal of a parking function.