Identifier
Images
=>
Cc0005;cc-rep-1Cc0009;cc-rep-3
[1]=>[1,0]=>[2,1]=>{{1,2}} [1,1]=>[1,0,1,0]=>[3,1,2]=>{{1,2,3}} [2]=>[1,1,0,0]=>[2,3,1]=>{{1,2,3}} [1,1,1]=>[1,0,1,0,1,0]=>[4,1,2,3]=>{{1,2,3,4}} [1,2]=>[1,0,1,1,0,0]=>[3,1,4,2]=>{{1,2,3,4}} [2,1]=>[1,1,0,0,1,0]=>[2,4,1,3]=>{{1,2,3,4}} [3]=>[1,1,1,0,0,0]=>[2,3,4,1]=>{{1,2,3,4}} [1,1,1,1]=>[1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>{{1,2,3,4,5}} [1,1,2]=>[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>{{1,2,3,4,5}} [1,2,1]=>[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>{{1,2,3,4,5}} [1,3]=>[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>{{1,2,3,4,5}} [2,1,1]=>[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>{{1,2,3,4,5}} [2,2]=>[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>{{1,2,3,4,5}} [3,1]=>[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>{{1,2,3,4,5}} [4]=>[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>{{1,2,3,4,5}} [1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>{{1,2,3,4,5,6}} [1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>{{1,2,3,4,5,6}} [1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>{{1,2,3,4,5,6}} [1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>{{1,2,3,4,5,6}} [1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>{{1,2,3,4,5,6}} [1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>{{1,2,3,4,5,6}} [1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>{{1,2,3,4,5,6}} [1,4]=>[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>{{1,2,3,4,5,6}} [2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>{{1,2,3,4,5,6}} [2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>{{1,2,3,4,5,6}} [2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}} [2,3]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>{{1,2,3,4,5,6}} [3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>{{1,2,3,4,5,6}} [3,2]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}} [4,1]=>[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}} [5]=>[1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}} [1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}} [1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}} [1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7}} [1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}} [1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>{{1,2,3,4,5,6,7}} [1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>{{1,2,3,4,5,6,7}} [1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>{{1,2,3,4,5,6,7}} [1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}} [1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7}} [1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>{{1,2,3,4,5,6,7}} [1,2,2,1]=>[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}} [1,2,3]=>[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}} [1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>{{1,2,3,4,5,6,7}} [1,3,2]=>[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}} [1,4,1]=>[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}} [1,5]=>[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}} [2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>{{1,2,3,4,5,6,7}} [2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>{{1,2,3,4,5,6,7}} [2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}} [2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>{{1,2,3,4,5,6,7}} [2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}} [2,2,2]=>[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}} [2,3,1]=>[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}} [2,4]=>[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}} [3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}} [3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>{{1,2,3,4,5,6,7}} [3,2,1]=>[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}} [3,3]=>[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}} [4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}} [4,2]=>[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}} [5,1]=>[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}} [6]=>[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}}
Map
bounce path
Description
The bounce path determined by an integer composition.
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].