ThreeRegularSimpleModules
The simple modules that are 3-regular.
✓ checked against that system · ! checked, with disagreements (hover a chip)FindStat
St001137via DyckPath✓ThreeRegularSimpleModules(path)The simple modules that are 3-regular.Typed signatures
| Type | Package | Applies |
|---|---|---|
(dyck_path) -> number | combinatorics | always |
Details
- Defined over
DyckPathas an expression in_x, evaluated by compute-engine — the definition IS the implementation. - Takes a
DyckPathand 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 St001137.
Definition
Epsil, as the implementation runs it.
on DyckPath, over _x
0 if Length(_x) < 1 else Apply(
(series: list<integer>) => Apply(
(dims: list<integer>) => Max(Sum(Map(Function(((1 if Apply(
(syzygy: list<integer>) => Max(Sum(Map(Function(Max(0, Min(1, w - 1 +
series[w] -
(syzygy[1] + syzygy[2]), Min(series[syzygy[1] + 1] -
syzygy[2], series[w]) -
(w - 1 +
series[w] -
(syzygy[1] + syzygy[2])) +
1)) -
Max(0, Min(1, w - 1 +
series[w] -
syzygy[1], Min(series[syzygy[1] + 1], series[w]) -
(w - 1 +
series[w] -
syzygy[1]) +
1)) +
Max(0, Min(1, w - 1 +
series[w] -
syzygy[1], Min(syzygy[2], series[w]) -
(w - 1 +
series[w] -
syzygy[1]) +
1)), w), Range(1, Length(_x) / 2 +
1))), 0),
Apply((target: integer) => Fold(
Function(Apply(
(entry: integer) => [a[1], a[2], a[3]] if a[2] == entry ||
a[3] == target else [a[1] + a[2], entry - a[2], a[3] + 1],
series[a[1] + 1],
), a, b),
[v - 1, 1, 0],
Range(1, Length(_x) / 2 +
1),
), 3 - 1),
) ==
1 else 0) if Fold(
Function(Apply((cursor: integer) => Apply((extent: integer) => Apply(
(extension: integer) => Apply((entry: integer) => Apply((found: integer) => [
cursor if extent == entry else cursor + extent,
extent if extent == entry else entry - extent,
a[3] if a[4] == 1 else a[5] + 1 if extension > 0 else a[3],
found,
a[5] + 1,
], 1 if a[4] == 1 ||
extension > 0 else 0), series[cursor + 1]),
Max(Sum(Map(Function(Max(0, Min(1, w - 1 +
series[w] -
(cursor + extent), Min(series[cursor + 1] -
extent, series[w]) -
(w - 1 +
series[w] -
(cursor + extent)) +
1)) -
Max(0, Min(1, w - 1 +
series[w] -
cursor, Min(series[cursor + 1], series[w]) -
(w - 1 +
series[w] -
cursor) +
1)) +
Max(0, Min(1, w - 1 +
series[w] -
cursor, Min(extent, series[w]) -
(w - 1 +
series[w] -
cursor) +
1)), w), Range(1, Length(_x) / 2 +
1))), 0),
), a[2]), a[1]), a, b),
[
v - 1,
1,
0,
1 if Max(Sum(Map(
Function(Max(0, Min(1, w - 1 +
series[w] -
(v - 1), Min(1, series[w]) -
(w - 1 +
series[w] -
(v - 1)) +
1)), w),
Range(1, Length(_x) / 2 +
1),
)), 0) >
0 else 0,
0,
],
Range(1, Length(_x) / 2 +
1),
)[3] ==
3 else 0) if dims[v] == 3 else 0, v), Range(1, Length(_x) / 2 +
1))), 0),
Map(
Function(Fold(
Function(Apply(
(entry: integer) => [a[1], a[2], a[3]] if a[2] == entry else [a[1] + a[2], entry - a[2], a[3] + 1],
series[a[1] + 1],
), a, b),
[v - 1, 1, 0],
Range(1, Length(_x) / 2 +
1),
)[3], v),
Range(
1,
Length(_x) /
2 +
1,
),
),
),
Apply(
(h: list<integer>) => Apply(
(ups: list<integer>) => Join(Map(
Function(h[ups[Length(_x) / 2 +
1 -
t]] +
1, t),
Range(1, Length(_x) / 2),
), [1]),
Filter(
Range(1, Length(_x)),
Function(_x[i] == 1, i),
),
),
Map(
Function(Sum(Map(
Function(
2 *
_x[k] - 1,
k,
),
Range(1, i),
)), i),
Range(1, Length(_x)),
),
),
)Examples
Properties #
About
| Examples | 5 |
|---|---|
| Crosswalk | FindStat |