BargraphPeakCount

Peaks of the bargraph with bars of these heights: a rise, level steps, then a fall.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000805via IntegerComposition✓↗

BargraphPeakCount(composition)Peaks of the bargraph with bars of these heights: a rise, level steps, then a fall.

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.
• Deutsch and Elizalde, A bijection between bargraphs and Dyck paths.

Definition

Epsil, as the implementation runs it.

on IntegerComposition, over _x

0 if Length(_x) < 1 else Fold(Function(
                                        [b, 1, a[3]] if b > a[1] else [
                                                                        b,
                                                                        0,
                                                                        a[3] +
                                                                        a[2],
                                                                      ] if b <
                                                                          a[1] else [b, a[2], a[3]],
                                        a,
                                        b,
                                      ), [0, 0, 0], Join(_x, [0]))[3]

Examples

Basic #

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

live ↗

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

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St000805

FindStat's value for [2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerComposition}}([2]), \text{BargraphPeakCount})$Out$1$

Known value · FindStat St000805

FindStat's value for [3]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerComposition}}([3]), \text{BargraphPeakCount})$Out$1$

Known value · FindStat St000805

About

Examples	4
Crosswalk	FindStat