- FindStat

Identifier

Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001128: Integer partitions ⟶ ℤ

Values

[1,0,1,1,0,0,1,0] => [2,1,4,3] => [2,2] => [2] => 1

[1,0,1,1,0,1,0,0] => [2,4,1,3] => [2,2] => [2] => 1

[1,1,0,1,0,0,1,0] => [3,1,4,2] => [2,2] => [2] => 1

[1,1,0,1,0,1,0,0] => [3,4,1,2] => [2,2] => [2] => 1

[1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => [3,2] => [2] => 1

[1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => [3,2] => [2] => 1

[1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => [3,2] => [2] => 1

[1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => [3,2] => [2] => 1

[1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => [3,2] => [2] => 1

[1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => [3,2] => [2] => 1

[1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => [3,2] => [2] => 1

[1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => [3,2] => [2] => 1

[1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => [3,2] => [2] => 1

[1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => [3,2] => [2] => 1

[1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => [3,2] => [2] => 1

[1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => [3,2] => [2] => 1

[1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => [3,2] => [2] => 1

[1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => [3,2] => [2] => 1

[1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => [3,2] => [2] => 1

[1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => [3,2] => [2] => 1

[1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => [3,2] => [2] => 1

[1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => [3,2] => [2] => 1

[1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => [3,2] => [2] => 1

[1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => [3,2] => [2] => 1

[1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => [3,2] => [2] => 1

[1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [3,2] => [2] => 1

[1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => [3,2] => [2] => 1

[1,1,1,0,1,0,0,1,0,0] => [4,1,5,2,3] => [3,2] => [2] => 1

[1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => [3,2] => [2] => 1

[1,0,1,0,1,0,1,1,0,0,1,0] => [2,3,4,1,6,5] => [4,2] => [2] => 1

[1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,4,6,1,5] => [4,2] => [2] => 1

[1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => [4,2] => [2] => 1

[1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => [4,2] => [2] => 1

[1,0,1,0,1,1,0,1,0,0,1,0] => [2,3,5,1,6,4] => [4,2] => [2] => 1

[1,0,1,0,1,1,0,1,0,1,0,0] => [2,3,5,6,1,4] => [4,2] => [2] => 1

[1,0,1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [4,2] => [2] => 1

[1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => [4,2] => [2] => 1

[1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => [4,2] => [2] => 1

[1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => [4,2] => [2] => 1

[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,5,6,3] => [4,2] => [2] => 1

[1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => [4,2] => [2] => 1

[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5] => [3,3] => [3] => 1

[1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => [3,3] => [3] => 1

[1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,5,6] => [4,2] => [2] => 1

[1,0,1,1,0,1,0,0,1,0,1,0] => [2,4,1,5,6,3] => [4,2] => [2] => 1

[1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => [4,2] => [2] => 1

[1,0,1,1,0,1,0,1,0,0,1,0] => [2,4,5,1,6,3] => [4,2] => [2] => 1

[1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,5,6,1,3] => [4,2] => [2] => 1

[1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [4,2] => [2] => 1

[1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => [3,3] => [3] => 1

[1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => [3,3] => [3] => 1

[1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => [3,3] => [3] => 1

[1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => [4,2] => [2] => 1

[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => [4,2] => [2] => 1

[1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,5,4,6] => [4,2] => [2] => 1

[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => [3,3] => [3] => 1

[1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => [3,3] => [3] => 1

[1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => [4,2] => [2] => 1

[1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => [3,3] => [3] => 1

[1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => [3,3] => [3] => 1

[1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => [3,3] => [3] => 1

[1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => [4,2] => [2] => 1

[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => [4,2] => [2] => 1

[1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => [4,2] => [2] => 1

[1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => [4,2] => [2] => 1

[1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => [4,2] => [2] => 1

[1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => [4,2] => [2] => 1

[1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,6,2,5] => [4,2] => [2] => 1

[1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => [4,2] => [2] => 1

[1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,6] => [4,2] => [2] => 1

[1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => [4,2] => [2] => 1

[1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,5,6,2,4] => [4,2] => [2] => 1

[1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [4,2] => [2] => 1

[1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,4,6,5] => [4,2] => [2] => 1

[1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => [4,2] => [2] => 1

[1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => [4,2] => [2] => 1

[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,4,5,6,2] => [4,2] => [2] => 1

[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,4,5,2,6] => [4,2] => [2] => 1

[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => [3,3] => [3] => 1

[1,1,0,1,0,0,1,1,0,1,0,0] => [3,1,4,6,2,5] => [3,3] => [3] => 1

[1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => [4,2] => [2] => 1

[1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,5,6,2] => [4,2] => [2] => 1

[1,1,0,1,0,1,0,0,1,1,0,0] => [3,4,1,5,2,6] => [4,2] => [2] => 1

[1,1,0,1,0,1,0,1,0,0,1,0] => [3,4,5,1,6,2] => [4,2] => [2] => 1

[1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,1,2] => [4,2] => [2] => 1

[1,1,0,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [4,2] => [2] => 1

[1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => [3,3] => [3] => 1

[1,1,0,1,0,1,1,0,0,1,0,0] => [3,4,1,6,2,5] => [3,3] => [3] => 1

[1,1,0,1,0,1,1,0,1,0,0,0] => [3,4,6,1,2,5] => [3,3] => [3] => 1

[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,2] => [2] => 1

[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => [4,2] => [2] => 1

[1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => [4,2] => [2] => 1

[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => [3,3] => [3] => 1

[1,1,0,1,1,0,0,1,0,1,0,0] => [3,1,5,6,2,4] => [3,3] => [3] => 1

[1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => [4,2] => [2] => 1

[1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => [3,3] => [3] => 1

[1,1,0,1,1,0,1,0,0,1,0,0] => [3,5,1,6,2,4] => [3,3] => [3] => 1

[1,1,0,1,1,0,1,0,1,0,0,0] => [3,5,6,1,2,4] => [3,3] => [3] => 1

[1,1,0,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4,6] => [4,2] => [2] => 1

[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => [4,2] => [2] => 1

[1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => [4,2] => [2] => 1

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search for individual values

searching the database for the individual values of this statistic

Description

The exponens consonantiae of a partition.
This is the quotient of the least common multiple and the greatest common divior of the parts of the partiton. See [1, Caput sextum, §19-§22].

Map

Robinson-Schensted tableau shape

Description

Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.

Map

to 321-avoiding permutation (Billey-Jockusch-Stanley)

Description

The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.

Map

first row removal

Description

Removes the first entry of an integer partition