Re: injective monotone functions on k-sets

In article <ft2uu6$k7h$1@xxxxxxxxxxxxxxxx>, edfromo@xxxxxxxxx wrote:

Let S be a set of size n, and let S^k and S^{k+1} denote the set of
subsets of S of size k and k+1 respectively. Given k, is it true that
for sufficiently large n, there is an injective function
f : S^k -> S^{k+1}
such that A \subset f(A) for all A in S^k?

Clearly this requires n \geq 2k+1 by cardinality considerations. Is
this condition sufficient?

(I am particularly interested in the case k = 3.)

Have you checked to see whether Hall's Marriage Theorem applies?

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)

.