SkewCornerCount
The cells that are an inner corner or an outer corner of the shape, counted once when both.
✓ checked against that system · ! checked, with disagreements (hover a chip)FindStat
St001488via SkewPartition✓SkewCornerCount(shape)The cells that are an inner corner or an outer corner of the shape, counted once when both.Typed signatures
| Type | Package | Applies |
|---|---|---|
(skew_partition) -> number | combinatorics | always |
Details
- Defined over
SkewPartitionas an expression in_x, evaluated by compute-engine — the definition IS the implementation. - Takes a
SkewPartitionand nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer. - FindStat's St001488, the removable cells of the skew partition: the union of its inner and outer corners. A row holding one cell can have the same cell as both. The empty shape gives 0.
Definition
Epsil, as the implementation runs it.
on SkewPartition, over _x
0 if Length(_x[1]) == 0 else Apply((lam: list<integer>) => Apply((raw: list<integer>) => Apply(
(mu: list<integer>) => Max(Sum(Map(Function((1 if i == 1 else 1 if mu[i - 1] >
mu[i] else 0) +
(1 if i == Length(lam) else 1 if lam[i] >
lam[i + 1] else 0) -
((1 if i == 1 else 1 if mu[i - 1] >
mu[i] else 0) *
(1 if i == Length(lam) else 1 if lam[i] >
lam[i + 1] else 0) if lam[i] ==
mu[i] + 1 else 0), i), Range(1, Length(lam)))), 0),
Map(
Function(raw[i] if i <= Length(raw) else 0, i),
Range(1, Length(lam)),
),
), _x[2]), _x[1])Examples
Properties #
About
| Examples | 4 |
|---|---|
| Crosswalk | FindStat |