Re: Comment on Math::Math_Combinatorics

I was thinking more of having repitition as an option.  Wiki
*said* the
definition can be either with or without repitition for both
combinations
and permutations.  (Now this is what I don't like about
wiki: Someone has
deleted the "Permutations without Repitition"
sub-section without even
providing a reason.  See the history tab)


>
> However, there's a topic to think about - repetitions.
The original
> definition of combination in mathematics implies that
the elements have
> to be unique, i.e. the combinations of the set {A, A,
B} are the same as
> these of {A, B}, of {A, A, A, A, B}, etc. Nevertheless,
the term
> "combination with repetition" exists. I will
try to take a look in my
> university courses on combinatorics during the weekend,
because I'm
> uncertain what is the correct behaviour that has to be
followed in the
> package.
>


-- 
    David Sanders
    shangxiao

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AFAIK repetition is a property of both combination or
permutation.
Combination is used when the order of the elements doesn't
matters
(like forming a team of 3 people from a set of 10 people,
ABC = CBA)
while permutation does (like generating a password, 123 !=
321). It is
not enough to know which one, combination or permutation, is
the right
one to solve your problem. You have to know if it is allowed
or not to
have repeated elements. So repetition is a
"property" (or a subform)
of both "tools".

Permutation with repetition:
Numeric password with 5 numbers: 10x10x10x10x10 = 100000
different passwords

Permutation without repetition:
Numeric password with 5 numbers: 10x9x8x7x6 = 30240
different passwords

Combination with repetition:
Subset of 2 people from a set of 3 people: C(2 3) * 2! = 6
(AA BB CC AB AC BC)

Combination without repetition:
Subset of 2 people from a set of 3 people: C(2 3) = 3 (AB AC
BC)

regards,
Igor.

On 3/30/07, David Sanders <dsandersbaselinesolutions.com.au> wrote:
>
> I was thinking more of having repitition as an option. 
Wiki *said* the
> definition can be either with or without repitition for
both combinations
> and permutations.  (Now this is what I don't like about
wiki: Someone has
> deleted the "Permutations without Repitition"
sub-section without even
> providing a reason.  See the history tab)
>
>
> >
> > However, there's a topic to think about -
repetitions. The original
> > definition of combination in mathematics implies
that the elements have
> > to be unique, i.e. the combinations of the set {A,
A, B} are the same as
> > these of {A, B}, of {A, A, A, A, B}, etc.
Nevertheless, the term
> > "combination with repetition" exists. I
will try to take a look in my
> > university courses on combinatorics during the
weekend, because I'm
> > uncertain what is the correct behaviour that has
to be followed in the
> > package.
> >
>
>
> --
>     David Sanders
>     shangxiao
>
> --
> PEAR Development Mailing List (http://pear.php.net/)
> To unsubscribe, visit: http://www.php.net/unsub
.php
>
>

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Just as a reference. For combinations and permutations there
exist some other
variations, for example the "Complete Permutation"
(or Derangement), and such
other weirdness.

See:

http://
mathworld.wolfram.com/Permutation.html
http://
mathworld.wolfram.com/Derangement.html
http://mathworld.wolfram.com/AlternatingPermutation.html

http://mathworld.wolfram.com/CircularPermutation.html
http://
mathworld.wolfram.com/Combination.html
http://mathworld.wolfram.com/BinomialCoefficient.html
... etc.

Caveat: I had not looked in detail at your package. My net
connection right now
is quite flaky.

Cheers.

--- David Sanders <dsandersbaselinesolutions.com.au> wrote:

> 
> I was thinking more of having repitition as an option. 
Wiki *said* the
> definition can be either with or without repitition for
both combinations
> and permutations.  (Now this is what I don't like about
wiki: Someone has
> deleted the "Permutations without Repitition"
sub-section without even
> providing a reason.  See the history tab)
> 
> 
> >
> > However, there's a topic to think about -
repetitions. The original
> > definition of combination in mathematics implies
that the elements have
> > to be unique, i.e. the combinations of the set {A,
A, B} are the same as
> > these of {A, B}, of {A, A, A, A, B}, etc.
Nevertheless, the term
> > "combination with repetition" exists. I
will try to take a look in my
> > university courses on combinatorics during the
weekend, because I'm
> > uncertain what is the correct behaviour that has
to be followed in the
> > package.
> >
> 
> 
> -- 
>     David Sanders
>     shangxiao
> 
> -- 
> PEAR Development Mailing List (http://pear.php.net/)
> To unsubscribe, visit: http://www.php.net/unsub
.php
> 
> 


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Web site: http://www.castagnetto.or
g/
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