Hello,

Can anyone help me understand how to derive the local LYM inequality from the LYM inequality?

Thanks in advance.

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- May 7th 2012, 02:46 PMhairymclairyAntichains and the LYM inequality
Hello,

Can anyone help me understand how to derive the local LYM inequality from the LYM inequality?

Thanks in advance. - May 7th 2012, 03:21 PMPlatoRe: Antichains and the LYM inequality
- May 8th 2012, 02:01 AMhairymclairyRe: Antichains and the LYM inequality
They're fairly standard theorems, I thought they'd be well-known as they trivially imply Sperner's theorem/lemma about the maximal size of an antichain.

The LYM inequality states that given an antichain on [n], let i.e the number of sets of size in Then

.

Now the local LYM inequality states that if then , where is the lower shadow of the antichain , in symbols .

In the above notation, . Each implies the other, but I'm struggling to show properly that the first inequality implies the second. - May 8th 2012, 06:57 AMhairymclairyRe: Antichains and the LYM inequality
I've solved this now.

Thanks anyway.