RibbonCornerCount

Corners of the ribbon: its inner and outer corners together.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001486via IntegerComposition✓↗

RibbonCornerCount(composition)Corners of the ribbon: its inner and outer corners together.

Typed signatures

Type	Package	Applies
(composition) -> number	combinatorics	always

Domain: Composition statistics

Details

• Defined over IntegerComposition as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a IntegerComposition and 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.

Definition

Epsil, as the implementation runs it.

on IntegerComposition, over _x

0 if Length(_x) < 1 else Count(Filter(
                                       Range(1, Length(_x)),
                                       Function(_x[i] >= 2, i),
                                     )) + (0 if Length(_x) < 2 else 1 +
                                                                   Count(Filter(
                                                                                 Range(1, Length(_x)),
                                                                                 Function(i >= 2 &&
                                                                                          i <=
                                                                                          Length(_x) - 1 &&
                                                                                          _x[i] >= 2, i),
                                                                               ))) + 1

Examples

Basic #

the composition $[2,1,3,1,1]$

live ↗

In$\mathrm{RibbonCornerCount}({\operatorname{IntegerComposition}}([2, 1, 3, 1, 1]))$Out$5$

Properties #

FindStat's value for [1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerComposition}}([1]), \text{RibbonCornerCount})$Out$1$

Known value · FindStat St001486

FindStat's value for [2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerComposition}}([2]), \text{RibbonCornerCount})$Out$2$

Known value · FindStat St001486

FindStat's value for [3]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerComposition}}([3]), \text{RibbonCornerCount})$Out$2$

Known value · FindStat St001486

About

Examples	4
Crosswalk	FindStat