Identifier
Mp00042:
Integer partitions
—initial tableau⟶
Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
Mp00134: Standard tableaux —descent word⟶ Binary words
Images
[1] => [[1]] =>
[2] => [[1,2]] => 0
[1,1] => [[1],[2]] => 1
[3] => [[1,2,3]] => 00
[2,1] => [[1,2],[3]] => 01
[1,1,1] => [[1],[2],[3]] => 11
[4] => [[1,2,3,4]] => 000
[3,1] => [[1,2,3],[4]] => 001
[2,2] => [[1,2],[3,4]] => 010
[2,1,1] => [[1,2],[3],[4]] => 011
[1,1,1,1] => [[1],[2],[3],[4]] => 111
[5] => [[1,2,3,4,5]] => 0000
[4,1] => [[1,2,3,4],[5]] => 0001
[3,2] => [[1,2,3],[4,5]] => 0010
[3,1,1] => [[1,2,3],[4],[5]] => 0011
[2,2,1] => [[1,2],[3,4],[5]] => 0101
[2,1,1,1] => [[1,2],[3],[4],[5]] => 0111
[1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111
[6] => [[1,2,3,4,5,6]] => 00000
[5,1] => [[1,2,3,4,5],[6]] => 00001
[4,2] => [[1,2,3,4],[5,6]] => 00010
[4,1,1] => [[1,2,3,4],[5],[6]] => 00011
[3,3] => [[1,2,3],[4,5,6]] => 00100
[3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[3,1,1,1] => [[1,2,3],[4],[5],[6]] => 00111
[2,2,2] => [[1,2],[3,4],[5,6]] => 01010
[2,2,1,1] => [[1,2],[3,4],[5],[6]] => 01011
[2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 01111
[1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111
[7] => [[1,2,3,4,5,6,7]] => 000000
[6,1] => [[1,2,3,4,5,6],[7]] => 000001
[5,2] => [[1,2,3,4,5],[6,7]] => 000010
[5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[4,3] => [[1,2,3,4],[5,6,7]] => 000100
[4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111
[8] => [[1,2,3,4,5,6,7,8]] => 0000000
[7,1] => [[1,2,3,4,5,6,7],[8]] => 0000001
[6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111
[9] => [[1,2,3,4,5,6,7,8,9]] => 00000000
[8,1] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[7,2] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[6,3] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[5,4] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 00001001
[5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 00001010
[5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 00001011
[5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 00010001
[4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 00010010
[4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 00010011
[4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 00010101
[4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 00010111
[4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111
[3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100
[3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 00100101
[3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 00100111
[3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 00101010
[3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 00101011
[3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 00101111
[3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 01010101
[2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 01010111
[2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 01011111
[2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111
[1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111
[10] => [[1,2,3,4,5,6,7,8,9,10]] => 000000000
[9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
>>> Load all 201 entries. <<<Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
Map
descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
searching the database
Sorry, this map was not found in the database.