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Forum index » Science and Technology » Math » Combinatorics
Terminology: How to describe a particular combinatorics problem
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David C1
science forum beginner


Joined: 21 Aug 2005
Posts: 1

PostPosted: Sun Aug 21, 2005 3:23 pm    Post subject: Re: Terminology: How to describe a particular combinatorics problem Reply with quote

On 20/08/05 10:49, Anonymous wrote:
Quote:
Could someone please help me with the following. What I really want to know
is what the correct *terminology* is for what I am trying to do, so that I
can then look up the appropriate section in a textbook or on Integer
Sequences etc.

An example is the following. How many ways there are to create 3-sized
subsets from the numbers 1 to 7 so that no two numbers appear in any subset.
Example

124
137
156
236
257
345
467

This counts for my purpose as just 1 arrangement. How many other
arrangements are there?

More generally, how many ways (distinct sets-of-subsets) are there to create
k-sized subsets from n objects so that no m<k objects appear in any subset
more than once. But as I said ... my main question is about the correct
description (terminology) for this problem!

Cheers,

Am I missing something here or isn't the required term

"combinations"? e.g. How many combinations are there of k objects
taken from n? IIRC, if you say "combinations" rather than
"arrangements" or "permutations" you are ignoring ordering, i.e.
257 is the same as 572. The answer is nCk = n!/((n-k!)k!). It is
the final k! on the bottom that deals with ordering.

Can't help you when you introduce m the same I'm afraid.


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| Central Somerset, UK. |
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Anonymous
Guest





PostPosted: Sun Aug 21, 2005 12:15 am    Post subject: Re: Terminology: How to describe a particular combinatorics problem Reply with quote

Tnak you Peter. I had not thought of looking at maximum distance codes.
Having now looked at some of the papers on maximum distance codes I
certainly see the connexion, but I can't quite see whether my problem is
identical to the quesition about number of maximum distance codes ... in
part because I'm not sure if 'maximum distance' refers to an arbitrarily
chosen distance, such as the "m" in my original post. Can you clarify it at
all?

Cheers

--
Mark R. Diamond


"Peter Webb" <webbfamily-diespamdie@optusnet.com.au> wrote in message
news:430755af$0$22591$afc38c87@news.optusnet.com.au...
Quote:

"Anonymous" <dot.dot@dot.dot.dot> wrote in message
news:de6uam$bh6$1@news-02.connect.com.au...
Could someone please help me with the following. What I really want to
know
is what the correct *terminology* is for what I am trying to do, so that
I
can then look up the appropriate section in a textbook or on Integer
Sequences etc.

An example is the following. How many ways there are to create 3-sized
subsets from the numbers 1 to 7 so that no two numbers appear in any
subset.
Example

124
137
156
236
257
345
467

This counts for my purpose as just 1 arrangement. How many other
arrangements are there?

More generally, how many ways (distinct sets-of-subsets) are there to
create
k-sized subsets from n objects so that no m<k objects appear in any
subset
more than once. But as I said ... my main question is about the correct
description (terminology) for this problem!

Cheers,

--
Mark R. Diamond




Googling "maximum distance codes" gave 54 hits, but these looked pretty
technical.

I don't think there is an explicit formula known for how many there are.

There's a related problem about how many lotto numbers combinations you
need
to guarantee (say) 4 out of 40, which I also seem to recall is unsolved.


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Peter Webb
science forum Guru Wannabe


Joined: 05 May 2005
Posts: 192

PostPosted: Sat Aug 20, 2005 2:09 pm    Post subject: Re: Terminology: How to describe a particular combinatorics problem Reply with quote

"Anonymous" <dot.dot@dot.dot.dot> wrote in message
news:de6uam$bh6$1@news-02.connect.com.au...
Quote:
Could someone please help me with the following. What I really want to
know
is what the correct *terminology* is for what I am trying to do, so that I
can then look up the appropriate section in a textbook or on Integer
Sequences etc.

An example is the following. How many ways there are to create 3-sized
subsets from the numbers 1 to 7 so that no two numbers appear in any
subset.
Example

124
137
156
236
257
345
467

This counts for my purpose as just 1 arrangement. How many other
arrangements are there?

More generally, how many ways (distinct sets-of-subsets) are there to
create
k-sized subsets from n objects so that no m<k objects appear in any subset
more than once. But as I said ... my main question is about the correct
description (terminology) for this problem!

Cheers,

--
Mark R. Diamond




Googling "maximum distance codes" gave 54 hits, but these looked pretty
technical.

I don't think there is an explicit formula known for how many there are.

There's a related problem about how many lotto numbers combinations you need
to guarantee (say) 4 out of 40, which I also seem to recall is unsolved.
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Anonymous
Guest





PostPosted: Sat Aug 20, 2005 7:49 am    Post subject: Terminology: How to describe a particular combinatorics problem Reply with quote

Could someone please help me with the following. What I really want to know
is what the correct *terminology* is for what I am trying to do, so that I
can then look up the appropriate section in a textbook or on Integer
Sequences etc.

An example is the following. How many ways there are to create 3-sized
subsets from the numbers 1 to 7 so that no two numbers appear in any subset.
Example

124
137
156
236
257
345
467

This counts for my purpose as just 1 arrangement. How many other
arrangements are there?

More generally, how many ways (distinct sets-of-subsets) are there to create
k-sized subsets from n objects so that no m<k objects appear in any subset
more than once. But as I said ... my main question is about the correct
description (terminology) for this problem!

Cheers,

--
Mark R. Diamond
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