The most elegant way to generate permutations in SQL server

Question

Given a the following table:

Index | Element
---------------
  1   |    A
  2   |    B
  3   |    C
  4   |    D

We want to generate all th

Answer 1

Simpler than a recursive CTE:

declare @Number Table( Element varchar(MAX), Id varchar(MAX) )
Insert Into @Number Values ( 'A', '01')
Insert Into @Number Values ( 'B', '02')
Insert Into @Number Values ( 'C', '03')
Insert Into @Number Values ( 'D', '04')

select a.Element, b.Element, c.Element, d.Element
from @Number a
join @Number b on b.Element not in (a.Element)
join @Number c on c.Element not in (a.Element, b.Element)
join @Number d on d.Element not in (a.Element, b.Element, c.Element)
order by 1, 2, 3, 4

For an arbitrary number of elements, script it out:

if object_id('tempdb..#number') is not null drop table #number
create table #number (Element char(1), Id int, Alias as '_'+convert(varchar,Id))
insert #number values ('A', 1)
insert #number values ('B', 2)
insert #number values ('C', 3)
insert #number values ('D', 4)
insert #number values ('E', 5)

declare @sql nvarchar(max)
set @sql = '
select '+stuff((
  select char(13)+char(10)+'+'+Alias+'.Element'
  from #number order by Id for xml path (''), type
  ).value('.','NVARCHAR(MAX)'),3,1,' ')

set @sql += '
from #number '+(select top 1 Alias from #number order by Id)

set @sql += (
  select char(13)+char(10)+'join #number '+Alias+' on '+Alias+'.Id not in ('
    +stuff((
      select ', '+Alias+'.Id'
      from #number b where a.Id > b.Id
      order by Id for xml path ('')
      ),1,2,'')
    + ')'
  from #number a where Id > (select min(Id) from #number)
  order by Element for xml path (''), type
  ).value('.','NVARCHAR(MAX)')

set @sql += '
order by 1'

print @sql
exec (@sql)

To generate this:

select 
 _1.Element
+_2.Element
+_3.Element
+_4.Element
+_5.Element
from #number _1
join #number _2 on _2.Id not in (_1.Id)
join #number _3 on _3.Id not in (_1.Id, _2.Id)
join #number _4 on _4.Id not in (_1.Id, _2.Id, _3.Id)
join #number _5 on _5.Id not in (_1.Id, _2.Id, _3.Id, _4.Id)
order by 1