Identifier
Mp00099: Dyck paths bounce pathDyck paths
Mp00222: Dyck paths peaks-to-valleysDyck paths
Mp00201: Dyck paths RingelPermutations
Mp00151: Permutations to cycle type Set partitions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0005;cc-rep-2Cc0009;cc-rep-4
[1,0]=>[1,0]=>[1,0]=>[2,1]=>{{1,2}} [1,0,1,0]=>[1,0,1,0]=>[1,1,0,0]=>[2,3,1]=>{{1,2,3}} [1,1,0,0]=>[1,1,0,0]=>[1,0,1,0]=>[3,1,2]=>{{1,2,3}} [1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>[2,3,4,1]=>{{1,2,3,4}} [1,0,1,1,0,0]=>[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[2,4,1,3]=>{{1,2,3,4}} [1,1,0,0,1,0]=>[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[3,1,4,2]=>{{1,2,3,4}} [1,1,0,1,0,0]=>[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[2,4,1,3]=>{{1,2,3,4}} [1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[1,1,0,1,0,0]=>[4,3,1,2]=>{{1,2,3,4}} [1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>{{1,2,3,4,5}} [1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>{{1,2,3,4,5}} [1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>{{1,2,3,4,5}} [1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>{{1,2,3,4,5}} [1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>{{1,2,3,4,5}} [1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>{{1,2,3,4,5}} [1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>{{1,2,3,4,5}} [1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>{{1,2,3,4,5}} [1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>{{1,2,3,4,5}} [1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>{{1,2,3,4,5}} [1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>{{1,2,3,4,5}} [1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>{{1,2,3,4,5}} [1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>{{1,2,3,4,5}} [1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>{{1,2,3,4,5}} [1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}} [1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}} [1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}} [1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}} [1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>{{1,2,3,4,5,6}} [1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>{{1,2,3,4,5,6}} [1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}} [1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}} [1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}} [1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>{{1,2,3,4,5,6}} [1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>{{1,2,3,4,5,6}} [1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}} [1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>{{1,2,3,4,5,6}} [1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>{{1,2,3,4,5,6}} [1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>{{1,2,3,4,5,6}} [1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>{{1,2,3,4,5,6}} [1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>{{1,2,3,4,5,6}} [1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>{{1,2,3,4,5,6}} [1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}} [1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>{{1,2,3,4,5,6}} [1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}} [1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>{{1,2,3,4,5,6}} [1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>{{1,2,3,4,5,6}} [1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}} [1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>{{1,2,3,4,5,6}} [1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>{{1,2,3,4,5,6}} [1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>{{1,2,3,4,5,6}} [1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>{{1,2,3,4,5,6}} [1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>{{1,2,3,4,5,6}} [1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>{{1,2,3,4,5,6}} [1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>{{1,2,3,4,5,6}} [1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>{{1,2,3,4,5,6}} [1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>{{1,2,3,4,5,6}} [1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>{{1,2,3,4,5,6}} [1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>{{1,2,3,4,5,6}} [1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>{{1,2,3,4,5,6}} [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>{{1,2,3,4,5,6,7}} [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}} [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>{{1,2,3,4,5,6,7}} [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}} [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}} [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}} [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>{{1,2,3,4,5,6,7}} [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]=>{{1,2,3,4,5,6,7}}
Map
bounce path
Description
Sends a Dyck path $D$ of length $2n$ to its bounce path.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
Map
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].