SkewPartition
A name from the enumeratio catalogue with no kernel of its own yet; this page carries its crosswalk only.
Catalogued in the enumeratio database; not yet written up here.
SkewPartition(...)Catalogued in the enumeratio database; not yet written up here.Typed signatures
| Type | Package | Applies |
|---|---|---|
(list<list<integer>>) -> skew_partition | combinatorics | always |
Statistics
On SkewPartition, called as CombinatorialStat(x, "Name").
- FirstRowMissingBoxCountSt001435The boxes of the first row that the shape leaves out: the first part of the inner partition.
- FrobeniusRankSt001597The fewest border strips that the shape divides into.
- InnerCornerCountSt001487The cells that can be added to the inner partition, within the rows of the shape.
- MaximalRookPlacementCountSt001660The ways to place as many non-attacking rooks as possible on the cells of the shape.
- MissingBoxCountSt001438The boxes of the outer partition that the shape leaves out: the size of the inner partition.
- RookPlacementCountSt001658The placements of any number of non-attacking rooks on the cells of the shape.
- SkewConnectedComponentCountSt001490The connected components of the shape: rows that start a component, the first row and every row that shares no column with the row above.
- SkewCornerCountSt001488The cells that are an inner corner or an outer corner of the shape, counted once when both.
- StandardTableauCountSt001595The standard Young tableaux of the shape: the ways to fill its cells with 1 .. n, rising along rows and down columns.
- TwoByTwoSquareCountSt001596The cells of the shape whose neighbors to the right, below and below to the right are also in it.
Maps
Into and out of SkewPartition, called as CombinatorialMap(x, "Name"). Properties are the laws we state and what FindStat records.
11 more in FindStat, not implemented here
- Mp00179IntegerPartition → SkewPartitionInjectionGraded mapto skew partition
- Mp00180IntegerComposition → SkewPartitionInjectionGraded mapto ribbon
- Mp00181SkewPartition → IntegerCompositionSurjectionGraded maprow lengths
- Mp00182SkewPartition → IntegerPartitionSurjectionouter shape
- Mp00183SkewPartition → IntegerPartitionSurjectioninner shape
- Mp00185SkewPartition → PosetsGraded mapcell poset
- Mp00186SkewPartition → IntegerPartitionSurjectionGraded mapdominating partition
- Mp00187SkewPartition → SkewPartitionBijectionInvolutionconjugate
- Mp00189SkewPartition → SkewPartitionGraded mapInvolutionrotate
- Mp00192SkewPartition → Latticesdominating sublattice
- Mp00233DyckPath → SkewPartitionInjectionskew partition
About
| Crosswalk | SageMath |
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