Identifier
Images
=>
Cc0002;cc-rep-0Cc0007;cc-rep-1
[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 [7,2,1]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>000000101 [7,1,1,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>000000111 [6,4]=>[[1,2,3,4,5,6],[7,8,9,10]]=>000001000 [6,3,1]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>000001001 [6,2,2]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>000001010 [6,2,1,1]=>[[1,2,3,4,5,6],[7,8],[9],[10]]=>000001011 [6,1,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>000001111 [5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000 [5,4,1]=>[[1,2,3,4,5],[6,7,8,9],[10]]=>000010001 [5,3,2]=>[[1,2,3,4,5],[6,7,8],[9,10]]=>000010010 [5,3,1,1]=>[[1,2,3,4,5],[6,7,8],[9],[10]]=>000010011 [5,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10]]=>000010101 [5,2,1,1,1]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]=>000010111 [5,1,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>000011111 [4,4,2]=>[[1,2,3,4],[5,6,7,8],[9,10]]=>000100010 [4,4,1,1]=>[[1,2,3,4],[5,6,7,8],[9],[10]]=>000100011 [4,3,3]=>[[1,2,3,4],[5,6,7],[8,9,10]]=>000100100 [4,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10]]=>000100101 [4,3,1,1,1]=>[[1,2,3,4],[5,6,7],[8],[9],[10]]=>000100111 [4,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>000101010 [4,2,2,1,1]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]=>000101011 [4,2,1,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>000101111 [4,1,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>000111111 [3,3,3,1]=>[[1,2,3],[4,5,6],[7,8,9],[10]]=>001001001 [3,3,2,2]=>[[1,2,3],[4,5,6],[7,8],[9,10]]=>001001010 [3,3,2,1,1]=>[[1,2,3],[4,5,6],[7,8],[9],[10]]=>001001011 [3,3,1,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>001001111 [3,2,2,2,1]=>[[1,2,3],[4,5],[6,7],[8,9],[10]]=>001010101 [3,2,2,1,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>001010111 [3,2,1,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>001011111 [3,1,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>001111111 [2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>010101010 [2,2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>010101011 [2,2,2,1,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>010101111 [2,2,1,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>010111111 [2,1,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>011111111 [1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>111111111 [6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>00000100000 [2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>01010101010
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 $1\leq i < n$.