ConstantRunCount

Maximal runs of equal parts.

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ConstantRunCount(composition)Maximal runs 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.
• Hopkins, Shattuck and Sills, Parts and subword patterns in compositions.

Definition

Epsil, as the implementation runs it.

on IntegerComposition, over _x

0 if Length(_x) < 1 else 1 + (0 if Length(_x) < 2 else Count(Filter(
                                                                     Range(
                                                                            1,
                                                                            Length(_x) -
                                                                            1,
                                                                          ),
                                                                     Function(Abs(_x[i + 1] -
                                                                                  _x[i]) >
                                                                              0, i),
                                                                   )))

Examples

Basic #

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

live ↗

In$\mathrm{ConstantRunCount}({\operatorname{IntegerComposition}}([2, 1, 3, 1, 1]))$Out$4$

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St000767

FindStat's value for [2]

live ↗

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

Known value · FindStat St000767

FindStat's value for [3]

live ↗

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

Known value · FindStat St000767

About

Examples	4
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