ShortestConstantRun

The length of the shortest run of equal parts.

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ShortestConstantRun(composition)The length of the shortest run of equal 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.

Definition

Epsil, as the implementation runs it.

on IntegerComposition, over _x

0 if Length(_x) < 1 else Min(Rest(Fold(
                                        Function(ReplaceAt(
                                                            a,
                                                            Length(a),
                                                            Last(a) + 1,
                                                          ) if b == a[1] else Join(
                                                                                   ReplaceAt(a, 1, b),
                                                                                   [1],
                                                                                 ), a, b),
                                        [0],
                                        _x,
                                      )))

Examples

Basic #

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

live ↗

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

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St000900

FindStat's value for [2]

live ↗

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

Known value · FindStat St000900

FindStat's value for [3]

live ↗

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

Known value · FindStat St000900

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