SmallestFixedPoint

The smallest i with p(i) = i, or n + 1 when there is none.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001468via Permutation✓

SmallestFixedPoint(p)The smallest i with p(i) = i, or n + 1 when there is none.

Typed signatures

Type	Package	Applies
`(permutation) -> number`	`combinatorics`	always

Domain: Permutation statistics

Details

Defined over Permutation as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
Takes a Permutation 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 Permutation, over _x

Min(Join(
          Filter(Range(1, Length(_x), 1), Function(_x[i] == i, i)),
          [Length(_x) + 1],
        ))

Basic #

the one-line word $312$

\mathrm{SmallestFixedPoint}({\operatorname{Permutation}}([3, 1, 2]))

Out

4

the one-line word $2413$

\mathrm{SmallestFixedPoint}({\operatorname{Permutation}}([2, 4, 1, 3]))

Out

5

Properties #

FindStat's value for [1]

\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1]), \text{SmallestFixedPoint})

Out

1

Known value · FindStat St001468

FindStat's value for [1,2]

\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1, 2]), \text{SmallestFixedPoint})

Out

1

Known value · FindStat St001468

FindStat's value for [2,1]

\mathrm{CombinatorialStat}({\operatorname{Permutation}}([2, 1]), \text{SmallestFixedPoint})

Out

3

Known value · FindStat St001468

About

Examples	5
Crosswalk	FindStat