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a subset of natural number
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levine121323@yahoo.com
science forum beginner


Joined: 21 Jul 2006
Posts: 1

PostPosted: Fri Jul 21, 2006 6:17 am    Post subject: a subset of natural number Reply with quote

Let A={a_i} and B={b_i} (i=[1,100]) be 2 sets natural numbers
(delivered randomly in range [1,10])
for example, i=8 then
A={1,2,5,6,7,8,5,6}
B={4,1,2,5,7,10,5,6}
I like to prove that there exists a repeated pattern of A in B that is
largest, in my example it is {1,2,5}
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David C. Ullrich
science forum Guru


Joined: 28 Apr 2005
Posts: 2250

PostPosted: Fri Jul 21, 2006 10:44 am    Post subject: Re: a subset of natural number Reply with quote

On 20 Jul 2006 23:17:07 -0700, levine121323@yahoo.com wrote:

Quote:
Let A={a_i} and B={b_i} (i=[1,100]) be 2 sets natural numbers
(delivered randomly in range [1,10])
for example, i=8 then
A={1,2,5,6,7,8,5,6}
B={4,1,2,5,7,10,5,6}
I like to prove that there exists a repeated pattern of A in B that is
largest, in my example it is {1,2,5}

First, you're not talking about sets, you're talking about
sequences.

Anyway, the existence of a largest repeated pattern from A in B
is obvious. Look at all the subsequences of A that appear in
B. There are only finitely many. One of them has maximal length.

(Maybe by "largest" you mean that it is _strictly_ longer than
any other repeated subsequence? You can't prove that because
it's easy to give examples where it's not true.)

************************

David C. Ullrich
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