Identifier
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Images
[1] => [[1],[]] => ([],1)
[2] => [[2],[]] => ([],1)
[1,1] => [[1,1],[]] => ([],1)
[3] => [[3],[]] => ([],1)
[2,1] => [[2,1],[]] => ([],1)
[1,1,1] => [[1,1,1],[]] => ([],1)
[4] => [[4],[]] => ([],1)
[3,1] => [[3,1],[]] => ([],1)
[2,2] => [[2,2],[]] => ([],1)
[2,1,1] => [[2,1,1],[]] => ([],1)
[1,1,1,1] => [[1,1,1,1],[]] => ([],1)
[5] => [[5],[]] => ([],1)
[4,1] => [[4,1],[]] => ([],1)
[3,2] => [[3,2],[]] => ([],1)
[3,1,1] => [[3,1,1],[]] => ([],1)
[2,2,1] => [[2,2,1],[]] => ([],1)
[2,1,1,1] => [[2,1,1,1],[]] => ([],1)
[1,1,1,1,1] => [[1,1,1,1,1],[]] => ([],1)
[6] => [[6],[]] => ([],1)
[5,1] => [[5,1],[]] => ([],1)
[4,2] => [[4,2],[]] => ([],1)
[4,1,1] => [[4,1,1],[]] => ([],1)
[3,3] => [[3,3],[]] => ([],1)
[3,2,1] => [[3,2,1],[]] => ([],1)
[3,1,1,1] => [[3,1,1,1],[]] => ([],1)
[2,2,2] => [[2,2,2],[]] => ([],1)
[2,2,1,1] => [[2,2,1,1],[]] => ([],1)
[2,1,1,1,1] => [[2,1,1,1,1],[]] => ([],1)
[1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => ([],1)
[7] => [[7],[]] => ([],1)
[6,1] => [[6,1],[]] => ([],1)
[5,2] => [[5,2],[]] => ([],1)
[5,1,1] => [[5,1,1],[]] => ([],1)
[4,3] => [[4,3],[]] => ([],1)
[4,2,1] => [[4,2,1],[]] => ([],1)
[4,1,1,1] => [[4,1,1,1],[]] => ([],1)
[3,3,1] => [[3,3,1],[]] => ([],1)
[3,2,2] => [[3,2,2],[]] => ([],1)
[3,2,1,1] => [[3,2,1,1],[]] => ([],1)
[3,1,1,1,1] => [[3,1,1,1,1],[]] => ([],1)
[2,2,2,1] => [[2,2,2,1],[]] => ([],1)
[2,2,1,1,1] => [[2,2,1,1,1],[]] => ([],1)
[2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => ([],1)
[1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => ([],1)
[8] => [[8],[]] => ([],1)
[7,1] => [[7,1],[]] => ([],1)
[6,2] => [[6,2],[]] => ([],1)
[6,1,1] => [[6,1,1],[]] => ([],1)
[5,3] => [[5,3],[]] => ([],1)
[5,2,1] => [[5,2,1],[]] => ([],1)
[5,1,1,1] => [[5,1,1,1],[]] => ([],1)
[4,4] => [[4,4],[]] => ([],1)
[4,3,1] => [[4,3,1],[]] => ([],1)
[4,2,2] => [[4,2,2],[]] => ([],1)
[4,2,1,1] => [[4,2,1,1],[]] => ([],1)
[4,1,1,1,1] => [[4,1,1,1,1],[]] => ([],1)
[3,3,2] => [[3,3,2],[]] => ([],1)
[3,3,1,1] => [[3,3,1,1],[]] => ([],1)
[3,2,2,1] => [[3,2,2,1],[]] => ([],1)
[3,2,1,1,1] => [[3,2,1,1,1],[]] => ([],1)
[3,1,1,1,1,1] => [[3,1,1,1,1,1],[]] => ([],1)
[2,2,2,2] => [[2,2,2,2],[]] => ([],1)
[2,2,2,1,1] => [[2,2,2,1,1],[]] => ([],1)
[2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => ([],1)
[2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]] => ([],1)
[1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => ([],1)
[9] => [[9],[]] => ([],1)
[8,1] => [[8,1],[]] => ([],1)
[7,2] => [[7,2],[]] => ([],1)
[7,1,1] => [[7,1,1],[]] => ([],1)
[6,3] => [[6,3],[]] => ([],1)
[6,2,1] => [[6,2,1],[]] => ([],1)
[6,1,1,1] => [[6,1,1,1],[]] => ([],1)
[5,4] => [[5,4],[]] => ([],1)
[5,3,1] => [[5,3,1],[]] => ([],1)
[5,2,2] => [[5,2,2],[]] => ([],1)
[5,2,1,1] => [[5,2,1,1],[]] => ([],1)
[5,1,1,1,1] => [[5,1,1,1,1],[]] => ([],1)
[4,4,1] => [[4,4,1],[]] => ([],1)
[4,3,2] => [[4,3,2],[]] => ([],1)
[4,3,1,1] => [[4,3,1,1],[]] => ([],1)
[4,2,2,1] => [[4,2,2,1],[]] => ([],1)
[4,2,1,1,1] => [[4,2,1,1,1],[]] => ([],1)
[4,1,1,1,1,1] => [[4,1,1,1,1,1],[]] => ([],1)
[3,3,3] => [[3,3,3],[]] => ([],1)
[3,3,2,1] => [[3,3,2,1],[]] => ([],1)
[3,3,1,1,1] => [[3,3,1,1,1],[]] => ([],1)
[3,2,2,2] => [[3,2,2,2],[]] => ([],1)
[3,2,2,1,1] => [[3,2,2,1,1],[]] => ([],1)
[3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => ([],1)
[3,1,1,1,1,1,1] => [[3,1,1,1,1,1,1],[]] => ([],1)
[2,2,2,2,1] => [[2,2,2,2,1],[]] => ([],1)
[2,2,2,1,1,1] => [[2,2,2,1,1,1],[]] => ([],1)
[2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]] => ([],1)
[2,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1],[]] => ([],1)
[1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] => ([],1)
[10] => [[10],[]] => ([],1)
[9,1] => [[9,1],[]] => ([],1)
[8,2] => [[8,2],[]] => ([],1)
[8,1,1] => [[8,1,1],[]] => ([],1)
[7,3] => [[7,3],[]] => ([],1)
>>> Load all 181 entries. <<<
[7,2,1] => [[7,2,1],[]] => ([],1)
[7,1,1,1] => [[7,1,1,1],[]] => ([],1)
[6,4] => [[6,4],[]] => ([],1)
[6,3,1] => [[6,3,1],[]] => ([],1)
[6,2,2] => [[6,2,2],[]] => ([],1)
[6,2,1,1] => [[6,2,1,1],[]] => ([],1)
[6,1,1,1,1] => [[6,1,1,1,1],[]] => ([],1)
[5,5] => [[5,5],[]] => ([],1)
[5,4,1] => [[5,4,1],[]] => ([],1)
[5,3,2] => [[5,3,2],[]] => ([],1)
[5,3,1,1] => [[5,3,1,1],[]] => ([],1)
[5,2,2,1] => [[5,2,2,1],[]] => ([],1)
[5,2,1,1,1] => [[5,2,1,1,1],[]] => ([],1)
[5,1,1,1,1,1] => [[5,1,1,1,1,1],[]] => ([],1)
[4,4,2] => [[4,4,2],[]] => ([],1)
[4,4,1,1] => [[4,4,1,1],[]] => ([],1)
[4,3,3] => [[4,3,3],[]] => ([],1)
[4,3,2,1] => [[4,3,2,1],[]] => ([],1)
[4,3,1,1,1] => [[4,3,1,1,1],[]] => ([],1)
[4,2,2,2] => [[4,2,2,2],[]] => ([],1)
[4,2,2,1,1] => [[4,2,2,1,1],[]] => ([],1)
[4,2,1,1,1,1] => [[4,2,1,1,1,1],[]] => ([],1)
[4,1,1,1,1,1,1] => [[4,1,1,1,1,1,1],[]] => ([],1)
[3,3,3,1] => [[3,3,3,1],[]] => ([],1)
[3,3,2,2] => [[3,3,2,2],[]] => ([],1)
[3,3,2,1,1] => [[3,3,2,1,1],[]] => ([],1)
[3,3,1,1,1,1] => [[3,3,1,1,1,1],[]] => ([],1)
[3,2,2,2,1] => [[3,2,2,2,1],[]] => ([],1)
[3,2,2,1,1,1] => [[3,2,2,1,1,1],[]] => ([],1)
[3,2,1,1,1,1,1] => [[3,2,1,1,1,1,1],[]] => ([],1)
[3,1,1,1,1,1,1,1] => [[3,1,1,1,1,1,1,1],[]] => ([],1)
[2,2,2,2,2] => [[2,2,2,2,2],[]] => ([],1)
[2,2,2,2,1,1] => [[2,2,2,2,1,1],[]] => ([],1)
[2,2,2,1,1,1,1] => [[2,2,2,1,1,1,1],[]] => ([],1)
[2,2,1,1,1,1,1,1] => [[2,2,1,1,1,1,1,1],[]] => ([],1)
[2,1,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1,1],[]] => ([],1)
[1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1],[]] => ([],1)
[6,5] => [[6,5],[]] => ([],1)
[5,5,1] => [[5,5,1],[]] => ([],1)
[5,4,2] => [[5,4,2],[]] => ([],1)
[5,3,3] => [[5,3,3],[]] => ([],1)
[4,4,3] => [[4,4,3],[]] => ([],1)
[4,4,2,1] => [[4,4,2,1],[]] => ([],1)
[4,3,3,1] => [[4,3,3,1],[]] => ([],1)
[4,3,2,2] => [[4,3,2,2],[]] => ([],1)
[3,3,3,2] => [[3,3,3,2],[]] => ([],1)
[3,2,2,2,2] => [[3,2,2,2,2],[]] => ([],1)
[6,6] => [[6,6],[]] => ([],1)
[5,5,2] => [[5,5,2],[]] => ([],1)
[5,4,3] => [[5,4,3],[]] => ([],1)
[4,4,4] => [[4,4,4],[]] => ([],1)
[4,4,3,1] => [[4,4,3,1],[]] => ([],1)
[4,4,2,2] => [[4,4,2,2],[]] => ([],1)
[4,3,3,2] => [[4,3,3,2],[]] => ([],1)
[3,3,3,3] => [[3,3,3,3],[]] => ([],1)
[3,3,3,2,1] => [[3,3,3,2,1],[]] => ([],1)
[3,3,2,2,2] => [[3,3,2,2,2],[]] => ([],1)
[2,2,2,2,2,2] => [[2,2,2,2,2,2],[]] => ([],1)
[5,5,3] => [[5,5,3],[]] => ([],1)
[5,4,4] => [[5,4,4],[]] => ([],1)
[4,4,4,1] => [[4,4,4,1],[]] => ([],1)
[4,4,3,2] => [[4,4,3,2],[]] => ([],1)
[4,3,3,3] => [[4,3,3,3],[]] => ([],1)
[3,3,3,3,1] => [[3,3,3,3,1],[]] => ([],1)
[3,3,3,2,2] => [[3,3,3,2,2],[]] => ([],1)
[5,5,4] => [[5,5,4],[]] => ([],1)
[4,4,4,2] => [[4,4,4,2],[]] => ([],1)
[4,4,3,3] => [[4,4,3,3],[]] => ([],1)
[3,3,3,3,2] => [[3,3,3,3,2],[]] => ([],1)
[5,5,5] => [[5,5,5],[]] => ([],1)
[5,5,4,1] => [[5,5,4,1],[]] => ([],1)
[4,4,4,3] => [[4,4,4,3],[]] => ([],1)
[3,3,3,3,3] => [[3,3,3,3,3],[]] => ([],1)
[5,5,5,1] => [[5,5,5,1],[]] => ([],1)
[4,4,4,4] => [[4,4,4,4],[]] => ([],1)
[4,4,4,3,1] => [[4,4,4,3,1],[]] => ([],1)
[3,3,3,3,3,1] => [[3,3,3,3,3,1],[]] => ([],1)
[4,4,4,4,1] => [[4,4,4,4,1],[]] => ([],1)
[4,4,4,4,4,1] => [[4,4,4,4,4,1],[]] => ([],1)
[5,5,5,5,1] => [[5,5,5,5,1],[]] => ([],1)
Map
to skew partition
Description
The partition regarded as a skew partition.
Map
dominating sublattice
Description
Return the sublattice of the dominance order induced by the support of the expansion of the skew Schur function into Schur functions.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the subposet of the dominance order whose elements are the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a lattice.
The example $\lambda = (5^2,4^2,1)$ and $\mu=(3,2)$ shows that this lattice is not a sublattice of the dominance order.