I'm not sure I understand your problem.

This

permutation($perm.$set[$_],@set[0..$_-1],@set[$_+1..$#set]) foreach (0..$#set);

• adds element at pos $_ to the new $perm ( i.e. $perm = $perm.$set[$_] )
• the new @set is composed by the slices of the remaining elements except position $_. The sliced arrays are flattened to elements and all swallowed by the new @set. (i.e. @set = (@set[0..$_-1],@set[$_+1..$#set]) )

Here some code to demonstrate it:

C:/Perl_524/bin\perl.exe -w d:/tmp/pm/permute.pl 
 1:
  2:a
   3:ab
    4:abc
     5:abcd
abcd
    4:abd
     5:abdc
abdc
   3:ac
    4:acb
     5:acbd
acbd
    4:acd
     5:acdb
acdb
   3:ad
    4:adb
     5:adbc
adbc
    4:adc
     5:adcb
adcb
  2:b
   3:ba
    4:bac
     5:bacd
bacd
    4:bad
     5:badc
badc
   3:bc
    4:bca
     5:bcad
bcad
    4:bcd
     5:bcda
bcda
   3:bd
    4:bda
     5:bdac
bdac
    4:bdc
     5:bdca
bdca
  2:c
   3:ca
    4:cab
     5:cabd
cabd
    4:cad
     5:cadb
cadb
   3:cb
    4:cba
     5:cbad
cbad
    4:cbd
     5:cbda
cbda
   3:cd
    4:cda
     5:cdab
cdab
    4:cdb
     5:cdba
cdba
  2:d
   3:da
    4:dab
     5:dabc
dabc
    4:dac
     5:dacb
dacb
   3:db
    4:dba
     5:dbac
dbac
    4:dbc
     5:dbca
dbca
   3:dc
    4:dca
     5:dcab
dcab
    4:dcb
     5:dcba
dcba

Compilation finished at Tue Dec  8 22:44:20
[download]

update

expanded explanation

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