LongestZigzag

The length of the longest stretch of steps that alternate between up and down.

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LongestZigzag(path)The length of the longest stretch of steps that alternate between up and down.

Typed signatures

Type	Package	Applies
(dyck_path) -> number	combinatorics	always

Domain: Dyck path statistics

Details

• Defined over DyckPath as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a DyckPath 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.
• Starts the count again at 1 on a repeated step; the accumulator is (best, current, previous step), with 2 for no previous step.

Definition

Epsil, as the implementation runs it.

on DyckPath, over _x

Fold(Function([a[1], 1, b] if a[3] == b else [
                                               Max([a[1], a[2] + 1]),
                                               a[2] + 1,
                                               b,
                                             ], a, b), [0, 0, 2], _x)[1]

Examples

Basic #

the step word $UUDDUD$

live ↗

In$\mathrm{LongestZigzag}({\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0]))$Out$3$

the step word $UDUUDD$

live ↗

In$\mathrm{LongestZigzag}({\operatorname{DyckPath}}([1, 0, 1, 1, 0, 0]))$Out$3$

Properties #

FindStat's value for [1,0,1,0]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{DyckPath}}([1, 0, 1, 0]), \text{LongestZigzag})$Out$4$

Known value · FindStat St000981

FindStat's value for [1,1,0,0]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{DyckPath}}([1, 1, 0, 0]), \text{LongestZigzag})$Out$2$

Known value · FindStat St000981

FindStat's value for [1,0,1,0,1,0]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{DyckPath}}([1, 0, 1, 0, 1, 0]), \text{LongestZigzag})$Out$6$

Known value · FindStat St000981

About

Examples	5
Crosswalk	FindStat