WeakDescentCount

Positions i with c(i) >= c(i+1).

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001777via IntegerComposition✓↗

WeakDescentCount(composition)Positions i with c(i) >= c(i+1).

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

Examples

Basic #

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

live ↗

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

Properties #

FindStat's value for [1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerComposition}}([1]), \text{WeakDescentCount})$Out$0$

Known value · FindStat St001777

FindStat's value for [2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerComposition}}([2]), \text{WeakDescentCount})$Out$0$

Known value · FindStat St001777

FindStat's value for [3]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{IntegerComposition}}([3]), \text{WeakDescentCount})$Out$0$

Known value · FindStat St001777

About

Examples	4
Crosswalk	FindStat