Identifier
Mp00223:
Permutations
—runsort⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00019: Binary trees —right rotate⟶ Binary trees
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00019: Binary trees —right rotate⟶ Binary trees
Images
=>
Cc0010;cc-rep-2Cc0010;cc-rep-3
[1]=>[1]=>[.,.]=>[.,.]
[1,2]=>[1,2]=>[.,[.,.]]=>[[.,.],.]
[2,1]=>[1,2]=>[.,[.,.]]=>[[.,.],.]
[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]=>[[.,[.,.]],.]
[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]=>[[[.,.],.],.]
[2,1,3]=>[1,3,2]=>[.,[[.,.],.]]=>[[[.,.],.],.]
[2,3,1]=>[1,2,3]=>[.,[.,[.,.]]]=>[[.,[.,.]],.]
[3,1,2]=>[1,2,3]=>[.,[.,[.,.]]]=>[[.,[.,.]],.]
[3,2,1]=>[1,2,3]=>[.,[.,[.,.]]]=>[[.,[.,.]],.]
[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[[.,[.,[.,.]]],.]
[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]=>[[.,[[.,.],.]],.]
[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]=>[[[.,.],[.,.]],.]
[1,3,4,2]=>[1,3,4,2]=>[.,[[.,.],[.,.]]]=>[[[.,.],[.,.]],.]
[1,4,2,3]=>[1,4,2,3]=>[.,[[.,[.,.]],.]]=>[[[.,[.,.]],.],.]
[1,4,3,2]=>[1,4,2,3]=>[.,[[.,[.,.]],.]]=>[[[.,[.,.]],.],.]
[2,1,3,4]=>[1,3,4,2]=>[.,[[.,.],[.,.]]]=>[[[.,.],[.,.]],.]
[2,1,4,3]=>[1,4,2,3]=>[.,[[.,[.,.]],.]]=>[[[.,[.,.]],.],.]
[2,3,1,4]=>[1,4,2,3]=>[.,[[.,[.,.]],.]]=>[[[.,[.,.]],.],.]
[2,3,4,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[[.,[.,[.,.]]],.]
[2,4,1,3]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]=>[[[.,.],[.,.]],.]
[2,4,3,1]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]=>[[.,[[.,.],.]],.]
[3,1,2,4]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]=>[[.,[[.,.],.]],.]
[3,1,4,2]=>[1,4,2,3]=>[.,[[.,[.,.]],.]]=>[[[.,[.,.]],.],.]
[3,2,1,4]=>[1,4,2,3]=>[.,[[.,[.,.]],.]]=>[[[.,[.,.]],.],.]
[3,2,4,1]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]=>[[.,[[.,.],.]],.]
[3,4,1,2]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[[.,[.,[.,.]]],.]
[3,4,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[[.,[.,[.,.]]],.]
[4,1,2,3]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[[.,[.,[.,.]]],.]
[4,1,3,2]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]=>[[[.,.],[.,.]],.]
[4,2,1,3]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]=>[[[.,.],[.,.]],.]
[4,2,3,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[[.,[.,[.,.]]],.]
[4,3,1,2]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[[.,[.,[.,.]]],.]
[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[[.,[.,[.,.]]],.]
[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[[.,[.,[[.,.],.]]],.]
[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[1,2,4,5,3]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[1,2,5,3,4]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[1,2,5,4,3]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]=>[[[.,.],[[.,.],.]],.]
[1,3,4,2,5]=>[1,3,4,2,5]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[1,3,4,5,2]=>[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[1,3,5,2,4]=>[1,3,5,2,4]=>[.,[[.,.],[[.,.],.]]]=>[[[.,.],[[.,.],.]],.]
[1,3,5,4,2]=>[1,3,5,2,4]=>[.,[[.,.],[[.,.],.]]]=>[[[.,.],[[.,.],.]],.]
[1,4,2,3,5]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[1,4,2,5,3]=>[1,4,2,5,3]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[1,4,3,2,5]=>[1,4,2,5,3]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[1,4,3,5,2]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[1,4,5,2,3]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[1,4,5,3,2]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[1,5,2,3,4]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[1,5,2,4,3]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]=>[[[.,[[.,.],.]],.],.]
[1,5,3,2,4]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]=>[[[.,[[.,.],.]],.],.]
[1,5,3,4,2]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[1,5,4,2,3]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[1,5,4,3,2]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[2,1,3,4,5]=>[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[2,1,3,5,4]=>[1,3,5,2,4]=>[.,[[.,.],[[.,.],.]]]=>[[[.,.],[[.,.],.]],.]
[2,1,4,3,5]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[2,1,4,5,3]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[2,1,5,3,4]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[2,1,5,4,3]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[2,3,1,4,5]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[2,3,1,5,4]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[2,3,4,1,5]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[2,3,4,5,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[2,3,5,1,4]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[2,3,5,4,1]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[[.,[.,[[.,.],.]]],.]
[2,4,1,3,5]=>[1,3,5,2,4]=>[.,[[.,.],[[.,.],.]]]=>[[[.,.],[[.,.],.]],.]
[2,4,1,5,3]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]=>[[[.,[[.,.],.]],.],.]
[2,4,3,1,5]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]=>[[[.,[[.,.],.]],.],.]
[2,4,3,5,1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[2,4,5,1,3]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[2,4,5,3,1]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[2,5,1,3,4]=>[1,3,4,2,5]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[2,5,1,4,3]=>[1,4,2,5,3]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[2,5,3,1,4]=>[1,4,2,5,3]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[2,5,3,4,1]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[2,5,4,1,3]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]=>[[[.,.],[[.,.],.]],.]
[2,5,4,3,1]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[3,1,2,4,5]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[3,1,2,5,4]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[3,1,4,2,5]=>[1,4,2,5,3]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[3,1,4,5,2]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[3,1,5,2,4]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]=>[[[.,[[.,.],.]],.],.]
[3,1,5,4,2]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[3,2,1,4,5]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[3,2,1,5,4]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[3,2,4,1,5]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]=>[[[.,[[.,.],.]],.],.]
[3,2,4,5,1]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[3,2,5,1,4]=>[1,4,2,5,3]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[3,2,5,4,1]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[3,4,1,2,5]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[3,4,1,5,2]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[3,4,2,1,5]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[3,4,2,5,1]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[3,4,5,1,2]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[3,4,5,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[3,5,1,2,4]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[3,5,1,4,2]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[3,5,2,1,4]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[3,5,2,4,1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[3,5,4,1,2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[[.,[.,[[.,.],.]]],.]
[3,5,4,2,1]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[[.,[.,[[.,.],.]]],.]
[4,1,2,3,5]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[[.,[.,[[.,.],.]]],.]
[4,1,2,5,3]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[4,1,3,2,5]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]=>[[[.,.],[[.,.],.]],.]
[4,1,3,5,2]=>[1,3,5,2,4]=>[.,[[.,.],[[.,.],.]]]=>[[[.,.],[[.,.],.]],.]
[4,1,5,2,3]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[4,1,5,3,2]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[4,2,1,3,5]=>[1,3,5,2,4]=>[.,[[.,.],[[.,.],.]]]=>[[[.,.],[[.,.],.]],.]
[4,2,1,5,3]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[4,2,3,1,5]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[4,2,3,5,1]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[[.,[.,[[.,.],.]]],.]
[4,2,5,1,3]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]=>[[[.,.],[[.,.],.]],.]
[4,2,5,3,1]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[4,3,1,2,5]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[4,3,1,5,2]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[4,3,2,1,5]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],.],.]
[4,3,2,5,1]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[[.,[[.,[.,.]],.]],.]
[4,3,5,1,2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[[.,[.,[[.,.],.]]],.]
[4,3,5,2,1]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[[.,[.,[[.,.],.]]],.]
[4,5,1,2,3]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[4,5,1,3,2]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[4,5,2,1,3]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[4,5,2,3,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[4,5,3,1,2]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[4,5,3,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[5,1,2,3,4]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[5,1,2,4,3]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[5,1,3,2,4]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[5,1,3,4,2]=>[1,3,4,2,5]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[5,1,4,2,3]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[5,1,4,3,2]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[5,2,1,3,4]=>[1,3,4,2,5]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[5,2,1,4,3]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[5,2,3,1,4]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[5,2,3,4,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[5,2,4,1,3]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[5,2,4,3,1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[5,3,1,2,4]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[5,3,1,4,2]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[5,3,2,1,4]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,.]],.]
[5,3,2,4,1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[[.,[[.,.],[.,.]]],.]
[5,3,4,1,2]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[5,3,4,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[5,4,1,2,3]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[5,4,1,3,2]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[5,4,2,1,3]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],.]
[5,4,2,3,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[5,4,3,1,2]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[5,4,3,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,.]]]],.]
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[[.,[.,[.,[[.,.],.]]]],.]
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,2,3,5,6,4]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[[.,[.,[[.,[.,.]],.]]],.]
[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[[.,[.,[[.,[.,.]],.]]],.]
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[[.,[[.,.],[.,[.,.]]]],.]
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[1,2,4,5,3,6]=>[1,2,4,5,3,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[[.,[[.,.],[.,[.,.]]]],.]
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[5,7,1,3,4,2,6]=>[1,3,4,2,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[5,7,1,3,4,6,2]=>[1,3,4,6,2,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
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[5,7,1,6,3,2,4]=>[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
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[5,7,3,1,6,2,4]=>[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
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[5,7,3,2,4,1,6]=>[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
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[6,4,7,3,5,1,2]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[6,4,7,3,5,2,1]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
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[6,4,7,5,3,1,2]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]
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[6,7,5,2,3,4,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
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[7,2,6,1,5,4,3]=>[1,5,2,6,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[7,2,6,3,1,4,5]=>[1,4,5,2,6,3,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[7,2,6,3,1,5,4]=>[1,5,2,6,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[7,2,6,3,4,1,5]=>[1,5,2,6,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[7,2,6,3,4,5,1]=>[1,2,6,3,4,5,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
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[7,2,6,5,1,3,4]=>[1,3,4,2,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
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[7,3,1,6,2,5,4]=>[1,6,2,5,3,4,7]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
[7,3,1,6,4,2,5]=>[1,6,2,5,3,4,7]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
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[7,3,1,6,5,2,4]=>[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
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[7,3,2,4,5,1,6]=>[1,6,2,4,5,3,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
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[7,3,2,5,1,6,4]=>[1,6,2,5,3,4,7]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
[7,3,2,5,4,1,6]=>[1,6,2,5,3,4,7]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
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[7,3,4,2,5,1,6]=>[1,6,2,5,3,4,7]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
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[7,5,1,6,2,4,3]=>[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[7,5,1,6,3,2,4]=>[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
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[7,5,2,1,3,4,6]=>[1,3,4,6,2,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
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[7,5,2,6,1,3,4]=>[1,3,4,2,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
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[7,5,3,1,6,2,4]=>[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
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[7,5,3,2,4,1,6]=>[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
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[7,6,4,5,1,2,3]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[7,6,4,5,1,3,2]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[7,6,4,5,2,1,3]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[7,6,4,5,2,3,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[7,6,4,5,3,1,2]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[7,6,4,5,3,2,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[7,6,5,1,2,3,4]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[7,6,5,1,2,4,3]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[7,6,5,1,3,2,4]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[7,6,5,1,3,4,2]=>[1,3,4,2,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[7,6,5,1,4,2,3]=>[1,4,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[7,6,5,1,4,3,2]=>[1,4,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[7,6,5,2,1,3,4]=>[1,3,4,2,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[7,6,5,2,1,4,3]=>[1,4,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[7,6,5,2,3,1,4]=>[1,4,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[7,6,5,2,3,4,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[7,6,5,2,4,1,3]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[7,6,5,2,4,3,1]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[7,6,5,3,1,2,4]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[7,6,5,3,1,4,2]=>[1,4,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[7,6,5,3,2,1,4]=>[1,4,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[7,6,5,3,2,4,1]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[7,6,5,3,4,1,2]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[7,6,5,3,4,2,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[7,6,5,4,1,3,2]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[7,6,5,4,2,1,3]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[8,7,5,6,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[8,6,7,5,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[8,5,6,7,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[7,8,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[7,8,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[6,7,8,5,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[5,6,7,8,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[5,7,6,8,1,3,2,4]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
right rotate
Description
Return the result of right rotation applied to a binary tree.
Right rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the left child of the root of $T$ is a node. Let $C$ be the right child of the root of $T$, and let $A$ and $B$ be the left and right children of the left child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the right rotation of $T$ is the binary tree in which the left child of the root is $A$, whereas the right child of the root is a node whose left and right children are $B$ and $C$.
Right rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the left child of the root of $T$ is a node. Let $C$ be the right child of the root of $T$, and let $A$ and $B$ be the left and right children of the left child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the right rotation of $T$ is the binary tree in which the left child of the root is $A$, whereas the right child of the root is a node whose left and right children are $B$ and $C$.
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