LongestAscent

The longest run of consecutive up steps.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000444via DyckPath✓↗

LongestAscent(path)The longest run of consecutive up steps.

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.

Definition

Epsil, as the implementation runs it.

on DyckPath, over _x

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

Examples

Basic #

the step word $UUDDUD$

live ↗

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

the step word $UDUUDD$

live ↗

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

Properties #

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

live ↗

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

Known value · FindStat St000444

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

live ↗

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

Known value · FindStat St000444

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

live ↗

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

Known value · FindStat St000444

About

Examples	5
Crosswalk	FindStat