Re: Can you find one-to-one function like this?
- From: israel@xxxxxxxxxxx (Robert Israel)
- Date: 4 May 2005 22:55:16 GMT
In article <1115220036.388836.158860@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<sangjeong.kim@xxxxxxxxx> wrote:
>Let S={1,2,...,n}.
>Let A be the set of subsets of S having k elements.
>Let B be the set of subsets of S having n-k elements.
>If 2k<n, then is there one-to-one function f : A --> B such that C is
>subset of f(C) for all C in A?
Hint: Use K\"onig's Theorem (also known as the Marriage Theorem).
Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
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