- FindStat

Identifier

Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words

Images

[(1,2)] => [2,1] => [1,2] => [2,1] => 0

[(1,2),(3,4)] => [2,1,4,3] => [1,2,3,4] => [2,3,4,1] => 000

[(1,3),(2,4)] => [3,4,1,2] => [1,3,2,4] => [2,4,3,1] => 000

[(1,4),(2,3)] => [3,4,2,1] => [1,3,2,4] => [2,4,3,1] => 000

[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 00000

[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => 00000

[(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => 00000

[(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => 00000

[(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => 00000

[(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => 00000

[(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => 00000

[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => 00000

[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => 00000

[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => 00000

[(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [1,2,3,5,4,6] => [2,3,4,6,5,1] => 00000

[(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => 00000

[(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => [1,4,2,5,3,6] => [2,4,6,3,5,1] => 00000

[(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => [1,4,3,6,2,5] => [2,6,4,3,1,5] => 00000

[(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [1,4,3,6,2,5] => [2,6,4,3,1,5] => 00000

[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [1,2,3,4,5,6,7,8] => [2,3,4,5,6,7,8,1] => 0000000

[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [1,3,2,4,5,6,7,8] => [2,4,3,5,6,7,8,1] => 0000000

[(1,4),(2,3),(5,6),(7,8)] => [3,4,2,1,6,5,8,7] => [1,3,2,4,5,6,7,8] => [2,4,3,5,6,7,8,1] => 0000000

[(1,5),(2,3),(4,6),(7,8)] => [3,5,2,6,1,4,8,7] => [1,3,2,5,4,6,7,8] => [2,4,3,6,5,7,8,1] => 0000000

[(1,6),(2,3),(4,5),(7,8)] => [3,5,2,6,4,1,8,7] => [1,3,2,5,4,6,7,8] => [2,4,3,6,5,7,8,1] => 0000000

[(1,7),(2,3),(4,5),(6,8)] => [3,5,2,7,4,8,1,6] => [1,3,2,5,4,7,6,8] => [2,4,3,6,5,8,7,1] => 0000000

[(1,8),(2,3),(4,5),(6,7)] => [3,5,2,7,4,8,6,1] => [1,3,2,5,4,7,6,8] => [2,4,3,6,5,8,7,1] => 0000000

[(1,8),(2,4),(3,5),(6,7)] => [4,5,7,2,3,8,6,1] => [1,4,2,5,3,7,6,8] => [2,4,6,3,5,8,7,1] => 0000000

[(1,7),(2,4),(3,5),(6,8)] => [4,5,7,2,3,8,1,6] => [1,4,2,5,3,7,6,8] => [2,4,6,3,5,8,7,1] => 0000000

[(1,6),(2,4),(3,5),(7,8)] => [4,5,6,2,3,1,8,7] => [1,4,2,5,3,6,7,8] => [2,4,6,3,5,7,8,1] => 0000000

[(1,5),(2,4),(3,6),(7,8)] => [4,5,6,2,1,3,8,7] => [1,4,2,5,3,6,7,8] => [2,4,6,3,5,7,8,1] => 0000000

[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [1,4,2,5,3,6,7,8] => [2,4,6,3,5,7,8,1] => 0000000

[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [1,3,2,5,4,6,7,8] => [2,4,3,6,5,7,8,1] => 0000000

[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [1,2,3,5,4,6,7,8] => [2,3,4,6,5,7,8,1] => 0000000

[(1,2),(3,6),(4,5),(7,8)] => [2,1,5,6,4,3,8,7] => [1,2,3,5,4,6,7,8] => [2,3,4,6,5,7,8,1] => 0000000

[(1,3),(2,6),(4,5),(7,8)] => [3,5,1,6,4,2,8,7] => [1,3,2,5,4,6,7,8] => [2,4,3,6,5,7,8,1] => 0000000

[(1,4),(2,6),(3,5),(7,8)] => [4,5,6,1,3,2,8,7] => [1,4,2,5,3,6,7,8] => [2,4,6,3,5,7,8,1] => 0000000

[(1,5),(2,6),(3,4),(7,8)] => [4,5,6,3,1,2,8,7] => [1,4,3,6,2,5,7,8] => [2,6,4,3,7,5,8,1] => 0000000

[(1,6),(2,5),(3,4),(7,8)] => [4,5,6,3,2,1,8,7] => [1,4,3,6,2,5,7,8] => [2,6,4,3,7,5,8,1] => 0000000

[(1,7),(2,5),(3,4),(6,8)] => [4,5,7,3,2,8,1,6] => [1,4,3,7,2,5,6,8] => [2,6,4,3,7,8,5,1] => 0000000

[(1,8),(2,5),(3,4),(6,7)] => [4,5,7,3,2,8,6,1] => [1,4,3,7,6,8,2,5] => [2,8,4,3,1,6,5,7] => 0000000

[(1,8),(2,6),(3,4),(5,7)] => [4,6,7,3,8,2,5,1] => [1,4,3,7,5,8,2,6] => [2,8,4,3,6,1,5,7] => 0000000

[(1,7),(2,6),(3,4),(5,8)] => [4,6,7,3,8,2,1,5] => [1,4,3,7,2,6,5,8] => [2,6,4,3,8,7,5,1] => 0000000

[(1,6),(2,7),(3,4),(5,8)] => [4,6,7,3,8,1,2,5] => [1,4,3,7,2,6,5,8] => [2,6,4,3,8,7,5,1] => 0000000

[(1,5),(2,7),(3,4),(6,8)] => [4,5,7,3,1,8,2,6] => [1,4,3,7,2,5,6,8] => [2,6,4,3,7,8,5,1] => 0000000

[(1,4),(2,7),(3,5),(6,8)] => [4,5,7,1,3,8,2,6] => [1,4,2,5,3,7,6,8] => [2,4,6,3,5,8,7,1] => 0000000

[(1,3),(2,7),(4,5),(6,8)] => [3,5,1,7,4,8,2,6] => [1,3,2,5,4,7,6,8] => [2,4,3,6,5,8,7,1] => 0000000

[(1,2),(3,7),(4,5),(6,8)] => [2,1,5,7,4,8,3,6] => [1,2,3,5,4,7,6,8] => [2,3,4,6,5,8,7,1] => 0000000

[(1,2),(3,8),(4,5),(6,7)] => [2,1,5,7,4,8,6,3] => [1,2,3,5,4,7,6,8] => [2,3,4,6,5,8,7,1] => 0000000

[(1,3),(2,8),(4,5),(6,7)] => [3,5,1,7,4,8,6,2] => [1,3,2,5,4,7,6,8] => [2,4,3,6,5,8,7,1] => 0000000

[(1,4),(2,8),(3,5),(6,7)] => [4,5,7,1,3,8,6,2] => [1,4,2,5,3,7,6,8] => [2,4,6,3,5,8,7,1] => 0000000

[(1,5),(2,8),(3,4),(6,7)] => [4,5,7,3,1,8,6,2] => [1,4,3,7,6,8,2,5] => [2,8,4,3,1,6,5,7] => 0000000

[(1,6),(2,8),(3,4),(5,7)] => [4,6,7,3,8,1,5,2] => [1,4,3,7,5,8,2,6] => [2,8,4,3,6,1,5,7] => 0000000

[(1,7),(2,8),(3,4),(5,6)] => [4,6,7,3,8,5,1,2] => [1,4,3,7,2,6,5,8] => [2,6,4,3,8,7,5,1] => 0000000

[(1,8),(2,7),(3,4),(5,6)] => [4,6,7,3,8,5,2,1] => [1,4,3,7,2,6,5,8] => [2,6,4,3,8,7,5,1] => 0000000

[(1,8),(2,7),(3,5),(4,6)] => [5,6,7,8,3,4,2,1] => [1,5,3,7,2,6,4,8] => [2,6,4,8,3,7,5,1] => 0000000

[(1,7),(2,8),(3,5),(4,6)] => [5,6,7,8,3,4,1,2] => [1,5,3,7,2,6,4,8] => [2,6,4,8,3,7,5,1] => 0000000

[(1,6),(2,8),(3,5),(4,7)] => [5,6,7,8,3,1,4,2] => [1,5,3,7,4,8,2,6] => [2,8,4,6,3,1,5,7] => 0000000

[(1,5),(2,8),(3,6),(4,7)] => [5,6,7,8,1,3,4,2] => [1,5,2,6,3,7,4,8] => [2,4,6,8,3,5,7,1] => 0000000

[(1,4),(2,8),(3,6),(5,7)] => [4,6,7,1,8,3,5,2] => [1,4,2,6,3,7,5,8] => [2,4,6,3,8,5,7,1] => 0000000

[(1,3),(2,8),(4,6),(5,7)] => [3,6,1,7,8,4,5,2] => [1,3,2,6,4,7,5,8] => [2,4,3,6,8,5,7,1] => 0000000

[(1,2),(3,8),(4,6),(5,7)] => [2,1,6,7,8,4,5,3] => [1,2,3,6,4,7,5,8] => [2,3,4,6,8,5,7,1] => 0000000

[(1,2),(3,7),(4,6),(5,8)] => [2,1,6,7,8,4,3,5] => [1,2,3,6,4,7,5,8] => [2,3,4,6,8,5,7,1] => 0000000

[(1,3),(2,7),(4,6),(5,8)] => [3,6,1,7,8,4,2,5] => [1,3,2,6,4,7,5,8] => [2,4,3,6,8,5,7,1] => 0000000

[(1,4),(2,7),(3,6),(5,8)] => [4,6,7,1,8,3,2,5] => [1,4,2,6,3,7,5,8] => [2,4,6,3,8,5,7,1] => 0000000

[(1,5),(2,7),(3,6),(4,8)] => [5,6,7,8,1,3,2,4] => [1,5,2,6,3,7,4,8] => [2,4,6,8,3,5,7,1] => 0000000

[(1,6),(2,7),(3,5),(4,8)] => [5,6,7,8,3,1,2,4] => [1,5,3,7,2,6,4,8] => [2,6,4,8,3,7,5,1] => 0000000

[(1,7),(2,6),(3,5),(4,8)] => [5,6,7,8,3,2,1,4] => [1,5,3,7,2,6,4,8] => [2,6,4,8,3,7,5,1] => 0000000

[(1,8),(2,6),(3,5),(4,7)] => [5,6,7,8,3,2,4,1] => [1,5,3,7,4,8,2,6] => [2,8,4,6,3,1,5,7] => 0000000

[(1,8),(2,5),(3,6),(4,7)] => [5,6,7,8,2,3,4,1] => [1,5,2,6,3,7,4,8] => [2,4,6,8,3,5,7,1] => 0000000

[(1,7),(2,5),(3,6),(4,8)] => [5,6,7,8,2,3,1,4] => [1,5,2,6,3,7,4,8] => [2,4,6,8,3,5,7,1] => 0000000

[(1,6),(2,5),(3,7),(4,8)] => [5,6,7,8,2,1,3,4] => [1,5,2,6,3,7,4,8] => [2,4,6,8,3,5,7,1] => 0000000

[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [1,5,2,6,3,7,4,8] => [2,4,6,8,3,5,7,1] => 0000000

[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [1,4,2,6,3,7,5,8] => [2,4,6,3,8,5,7,1] => 0000000

[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [1,3,2,6,4,7,5,8] => [2,4,3,6,8,5,7,1] => 0000000

[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [1,2,3,6,4,7,5,8] => [2,3,4,6,8,5,7,1] => 0000000

[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [1,2,3,5,4,7,6,8] => [2,3,4,6,5,8,7,1] => 0000000

[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [1,3,2,5,4,7,6,8] => [2,4,3,6,5,8,7,1] => 0000000

[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [1,4,2,5,3,7,6,8] => [2,4,6,3,5,8,7,1] => 0000000

[(1,5),(2,4),(3,7),(6,8)] => [4,5,7,2,1,8,3,6] => [1,4,2,5,3,7,6,8] => [2,4,6,3,5,8,7,1] => 0000000

[(1,6),(2,4),(3,7),(5,8)] => [4,6,7,2,8,1,3,5] => [1,4,2,6,3,7,5,8] => [2,4,6,3,8,5,7,1] => 0000000

[(1,7),(2,4),(3,6),(5,8)] => [4,6,7,2,8,3,1,5] => [1,4,2,6,3,7,5,8] => [2,4,6,3,8,5,7,1] => 0000000

[(1,8),(2,4),(3,6),(5,7)] => [4,6,7,2,8,3,5,1] => [1,4,2,6,3,7,5,8] => [2,4,6,3,8,5,7,1] => 0000000

[(1,8),(2,3),(4,6),(5,7)] => [3,6,2,7,8,4,5,1] => [1,3,2,6,4,7,5,8] => [2,4,3,6,8,5,7,1] => 0000000

[(1,7),(2,3),(4,6),(5,8)] => [3,6,2,7,8,4,1,5] => [1,3,2,6,4,7,5,8] => [2,4,3,6,8,5,7,1] => 0000000

[(1,6),(2,3),(4,7),(5,8)] => [3,6,2,7,8,1,4,5] => [1,3,2,6,4,7,5,8] => [2,4,3,6,8,5,7,1] => 0000000

[(1,5),(2,3),(4,7),(6,8)] => [3,5,2,7,1,8,4,6] => [1,3,2,5,4,7,6,8] => [2,4,3,6,5,8,7,1] => 0000000

[(1,4),(2,3),(5,7),(6,8)] => [3,4,2,1,7,8,5,6] => [1,3,2,4,5,7,6,8] => [2,4,3,5,6,8,7,1] => 0000000

[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [1,3,2,4,5,7,6,8] => [2,4,3,5,6,8,7,1] => 0000000

[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [1,2,3,4,5,7,6,8] => [2,3,4,5,6,8,7,1] => 0000000

[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,7,8,6,5] => [1,2,3,4,5,7,6,8] => [2,3,4,5,6,8,7,1] => 0000000

[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,7,8,6,5] => [1,3,2,4,5,7,6,8] => [2,4,3,5,6,8,7,1] => 0000000

[(1,4),(2,3),(5,8),(6,7)] => [3,4,2,1,7,8,6,5] => [1,3,2,4,5,7,6,8] => [2,4,3,5,6,8,7,1] => 0000000

[(1,5),(2,3),(4,8),(6,7)] => [3,5,2,7,1,8,6,4] => [1,3,2,5,4,7,6,8] => [2,4,3,6,5,8,7,1] => 0000000

[(1,6),(2,3),(4,8),(5,7)] => [3,6,2,7,8,1,5,4] => [1,3,2,6,4,7,5,8] => [2,4,3,6,8,5,7,1] => 0000000

[(1,7),(2,3),(4,8),(5,6)] => [3,6,2,7,8,5,1,4] => [1,3,2,6,5,8,4,7] => [2,4,3,8,6,5,1,7] => 0000000

[(1,8),(2,3),(4,7),(5,6)] => [3,6,2,7,8,5,4,1] => [1,3,2,6,5,8,4,7] => [2,4,3,8,6,5,1,7] => 0000000

[(1,8),(2,4),(3,7),(5,6)] => [4,6,7,2,8,5,3,1] => [1,4,2,6,5,8,3,7] => [2,4,8,3,6,5,1,7] => 0000000

[(1,7),(2,4),(3,8),(5,6)] => [4,6,7,2,8,5,1,3] => [1,4,2,6,5,8,3,7] => [2,4,8,3,6,5,1,7] => 0000000

[(1,6),(2,4),(3,8),(5,7)] => [4,6,7,2,8,1,5,3] => [1,4,2,6,3,7,5,8] => [2,4,6,3,8,5,7,1] => 0000000

[(1,5),(2,4),(3,8),(6,7)] => [4,5,7,2,1,8,6,3] => [1,4,2,5,3,7,6,8] => [2,4,6,3,5,8,7,1] => 0000000

[(1,4),(2,5),(3,8),(6,7)] => [4,5,7,1,2,8,6,3] => [1,4,2,5,3,7,6,8] => [2,4,6,3,5,8,7,1] => 0000000

>>> Load all 131 entries. <<<

[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,7,2,8,6,4] => [1,3,2,5,4,7,6,8] => [2,4,3,6,5,8,7,1] => 0000000

[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,7,3,8,6,4] => [1,2,3,5,4,7,6,8] => [2,3,4,6,5,8,7,1] => 0000000

[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,7,8,3,5,4] => [1,2,3,6,4,7,5,8] => [2,3,4,6,8,5,7,1] => 0000000

[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,7,8,2,5,4] => [1,3,2,6,4,7,5,8] => [2,4,3,6,8,5,7,1] => 0000000

[(1,4),(2,6),(3,8),(5,7)] => [4,6,7,1,8,2,5,3] => [1,4,2,6,3,7,5,8] => [2,4,6,3,8,5,7,1] => 0000000

[(1,5),(2,6),(3,8),(4,7)] => [5,6,7,8,1,2,4,3] => [1,5,2,6,3,7,4,8] => [2,4,6,8,3,5,7,1] => 0000000

[(1,6),(2,5),(3,8),(4,7)] => [5,6,7,8,2,1,4,3] => [1,5,2,6,3,7,4,8] => [2,4,6,8,3,5,7,1] => 0000000

[(1,7),(2,5),(3,8),(4,6)] => [5,6,7,8,2,4,1,3] => [1,5,2,6,4,8,3,7] => [2,4,8,6,3,5,1,7] => 0000000

[(1,8),(2,5),(3,7),(4,6)] => [5,6,7,8,2,4,3,1] => [1,5,2,6,4,8,3,7] => [2,4,8,6,3,5,1,7] => 0000000

[(1,8),(2,6),(3,7),(4,5)] => [5,6,7,8,4,2,3,1] => [1,5,4,8,2,6,3,7] => [2,6,8,4,3,7,1,5] => 0000000

[(1,7),(2,6),(3,8),(4,5)] => [5,6,7,8,4,2,1,3] => [1,5,4,8,3,7,2,6] => [2,8,6,4,3,1,7,5] => 0000000

[(1,6),(2,7),(3,8),(4,5)] => [5,6,7,8,4,1,2,3] => [1,5,4,8,3,7,2,6] => [2,8,6,4,3,1,7,5] => 0000000

[(1,5),(2,7),(3,8),(4,6)] => [5,6,7,8,1,4,2,3] => [1,5,2,6,4,8,3,7] => [2,4,8,6,3,5,1,7] => 0000000

[(1,4),(2,7),(3,8),(5,6)] => [4,6,7,1,8,5,2,3] => [1,4,2,6,5,8,3,7] => [2,4,8,3,6,5,1,7] => 0000000

[(1,3),(2,7),(4,8),(5,6)] => [3,6,1,7,8,5,2,4] => [1,3,2,6,5,8,4,7] => [2,4,3,8,6,5,1,7] => 0000000

[(1,2),(3,7),(4,8),(5,6)] => [2,1,6,7,8,5,3,4] => [1,2,3,6,5,8,4,7] => [2,3,4,8,6,5,1,7] => 0000000

[(1,2),(3,8),(4,7),(5,6)] => [2,1,6,7,8,5,4,3] => [1,2,3,6,5,8,4,7] => [2,3,4,8,6,5,1,7] => 0000000

[(1,3),(2,8),(4,7),(5,6)] => [3,6,1,7,8,5,4,2] => [1,3,2,6,5,8,4,7] => [2,4,3,8,6,5,1,7] => 0000000

[(1,4),(2,8),(3,7),(5,6)] => [4,6,7,1,8,5,3,2] => [1,4,2,6,5,8,3,7] => [2,4,8,3,6,5,1,7] => 0000000

[(1,5),(2,8),(3,7),(4,6)] => [5,6,7,8,1,4,3,2] => [1,5,2,6,4,8,3,7] => [2,4,8,6,3,5,1,7] => 0000000

[(1,6),(2,8),(3,7),(4,5)] => [5,6,7,8,4,1,3,2] => [1,5,4,8,2,6,3,7] => [2,6,8,4,3,7,1,5] => 0000000

[(1,7),(2,8),(3,6),(4,5)] => [5,6,7,8,4,3,1,2] => [1,5,4,8,2,6,3,7] => [2,6,8,4,3,7,1,5] => 0000000

[(1,8),(2,7),(3,6),(4,5)] => [5,6,7,8,4,3,2,1] => [1,5,4,8,2,6,3,7] => [2,6,8,4,3,7,1,5] => 0000000

[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [2,3,4,5,6,7,8,9,10,1] => 000000000

[(1,10),(2,3),(4,5),(6,7),(8,9)] => [3,5,2,7,4,9,6,10,8,1] => [1,3,2,5,4,7,6,9,8,10] => [2,4,3,6,5,8,7,10,9,1] => 000000000

[(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => [1,2,3,5,4,6,7,8,9,10] => [2,3,4,6,5,7,8,9,10,1] => 000000000

[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,5,6,4,3,8,7,10,9] => [1,2,3,5,4,6,7,8,9,10] => [2,3,4,6,5,7,8,9,10,1] => 000000000

[(1,3),(2,5),(4,7),(6,9),(8,10)] => [3,5,1,7,2,9,4,10,6,8] => [1,3,2,5,4,7,6,9,8,10] => [2,4,3,6,5,8,7,10,9,1] => 000000000

[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [1,2,3,4,5,6,7,9,8,10] => [2,3,4,5,6,7,8,10,9,1] => 000000000

[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,9,10,8,7] => [1,2,3,4,5,6,7,9,8,10] => [2,3,4,5,6,7,8,10,9,1] => 000000000

Map

non-nesting-exceedence permutation

Description

The fixed-point-free permutation with deficiencies given by the perfect matching, no alignments and no inversions between exceedences.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.

Map

cycle-as-one-line notation

Description

Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.

Map

Kreweras complement

Description

Sends the permutation

$\pi \in \mathfrak{S}_n$ to the permutation

$\pi^{-1}c$ where

$c = (1,\ldots,n)$ is the long cycle.

Map

connectivity set

Description

The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is

$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$
For

$n > 1$ it can also be described as the set of occurrences of the mesh pattern

$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$
or equivalently

$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$
see [3].
The permutation is connected, when the connectivity set is empty.