LongestWeaklyIncreasingSubsequence

The length of a longest weakly increasing subsequence of the parts.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000757via IntegerComposition✓↗

LongestWeaklyIncreasingSubsequence(composition)The length of a longest weakly increasing subsequence of the parts.

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.
• The first row of the RSK shape of the composition as a word.

Definition

Epsil, as the implementation runs it.

on IntegerComposition, over _x

0 if Length(_x) < 1 else Count(Fold(Function(Apply(
                                                    Function(
                                                              Join(a, [b]) if m >
                                                                              Count(a) else ReplaceAt(a, m, b),
                                                              m,
                                                            ),
                                                    Count(Filter(
                                                                  a,
                                                                  Function(t <=
                                                                           b, t),
                                                                )) + 1,
                                                  ), a, b), [], _x))

Examples

Basic #

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

live ↗

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

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St000757

FindStat's value for [2]

live ↗

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

Known value · FindStat St000757

FindStat's value for [3]

live ↗

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

Known value · FindStat St000757

About

Examples	4
Crosswalk	FindStat