BargraphUpStepCount

Up steps of the bargraph.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000808via IntegerComposition✓↗

BargraphUpStepCount(composition)Up steps of the bargraph.

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 _x[1] + (0 if Length(_x) < 2 else Sum(Map(
                                                                    Function(_x[i + 1] -
                                                                             _x[i] if _x[i + 1] >
                                                                                 _x[i] else 0, i),
                                                                    Range(
                                                                           1,
                                                                           Length(_x) -
                                                                           1,
                                                                         ),
                                                                  )))

Examples

Basic #

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

live ↗

In$\mathrm{BargraphUpStepCount}({\operatorname{IntegerComposition}}([2, 1, 3, 1, 1]))$Out$4$

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St000808

FindStat's value for [2]

live ↗

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

Known value · FindStat St000808

FindStat's value for [3]

live ↗

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

Known value · FindStat St000808

About

Examples	4
Crosswalk	FindStat