A generalization of the AZ identity
نویسندگان
چکیده
We associate with every ~ c 2 ~ the upset U(~) = {U c gt : U D E for some E E ~} and the downset ~ ) ( 8 ) {D c ~ : D C E for some E C $}. W h e n ~d is an antichain in the poset (2 ~, D), then the identi ty becomes 1 w a ( x ) = 1. (1) ~ ~ + ~ Ixl(,;~,------5 xe~ (Ixr) xeu(~)\~ The LYM inequality is obtained by omission of the second summand, which by definition of W~ can also be wri t ten in the form x~ ' ( .4 ) Ix l ( l~ l ) " We call this the deficiency of the inequality. More generally, in [2] the Bollobds inequali ty was lifted to an identity.
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عنوان ژورنال:
- Combinatorica
دوره 13 شماره
صفحات -
تاریخ انتشار 1993