Version 6 of Combinatorial mathematics functions

Combinatorial mathematics deals with, among other things, functions dealing with calculating or displaying the number of combinations one can have of 10 things taken two at a time, etc. then help me word it.

AM In school I learned the following meanings for the expressions "permutation", "variation" and "combination":

permutation: An ordering of a set of N elements where the order is significant. variation: A subset of M elements out of N elements (M lower or equal N) where the order is significant. combination: A subset of M elements out of N elements where the order is not significant.

Simple formulae exist to calculate the number of permutations, variations and combinations, given N and M:

Number of permutations: N! (N faculty)

Number of variations: N!/M!

Number of combinations: N!/M!(N-M)!

So, the procedure "permutations" below is actually a procedure to return the variations. But if M == N, there is no difference.

(Note: small correction in "permutations" - "subsets2" was called instead of "permutations")

This came up on c.l.t so searching around the wiki I found some info atPower set of a list as well, but when searching, I found this page first (as I assume others would) so here is a copy stolen from there (was subsets2 on that page):

 proc combinations { list size } {
     if { $size == 0 } {
         return [list [list]]
     }
     set retval {}
     for { set i 0 } { ($i + $size) <= [llength $list] } { incr i } {
         set firstElement [lindex $list $i]
         set remainingElements [lrange $list [expr { $i + 1 }] end]
         foreach subset [combinations $remainingElements [expr { $size - 1 }]] {
             lappend retval [linsert $subset 0 $firstElement]
         }
     }
     return $retval
 }

If order of elements is meaningfull then you would want permutations so here is a proc to do that:

 proc permutations { list size } {
     if { $size == 0 } {
         return [list [list]]
     }
     set retval {}
     for { set i 0 } { $i < [llength $list] } { incr i } {
         set firstElement [lindex $list $i]
         set remainingElements [lreplace $list $i $i]
         foreach subset [permutations $remainingElements [expr { $size - 1 }]] {
             lappend retval [linsert $subset 0 $firstElement]
         }
     }
     return $retval
 }

And if you do want the power set you could use the nice version by Kevin Kenny presented on that page or make use of the combinations proc above:

 proc powerset {list} {
    for {set i 0} {$i <= [llength $list]} {incr i} {
        lappend ret [combinations $list $i]
    }
    return $ret
 }