LowerMiddleEntry

The entry p(floor((n+1)/2)).

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001807via Permutation✓

LowerMiddleEntry(p)The entry p(floor((n+1)/2)).

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

0 if Length(_x) < 1 else _x[(Length(_x) + 1 - (Length(_x) + 1) % 2) / 2]

Basic #

the one-line word $312$

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

Out

1

the one-line word $2413$

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

Out

4

Properties #

FindStat's value for [1]

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

Out

1

Known value · FindStat St001807

FindStat's value for [1,2]

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

Out

1

Known value · FindStat St001807

FindStat's value for [2,1]

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

Out

2

Known value · FindStat St001807

About

Examples	5
Crosswalk	FindStat