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\noindent{\bf Jin Qian and  Dijen K. Ray-Chaudhuri}
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{\bf Frankl-F\"uredi Type Inequalities 
for Polynomial Semi-lattices}
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Let $X$ be an $n$-set and $L$ a set of nonnegative integers.
 ${\cal F}$, a set of subsets of $X$, is said to be  an $L$ 
-intersection family if and only if for all $E \neq F \in {\cal F}, \,
|E \cap F | \in L$.  A special case of a conjecture of Frankl and 
F\"uredi 
states that 
if $ L = \{1, 2, \dots,k\}$,$ k$ a positive integer, then
$|{\cal F}| \leq\sum_{i=0}^{k}{n-1\choose i}$.

Here $|{\cal F}|$ denotes the number of elements in ${\cal F}$.

Recently Ramanan proved this conjecture.
  We extend his method to polynomial semi-lattices and we
also study some special $L$-intersection families on polynomial semi-lattices.

Finally we prove two modular versions of Ray-Chaudhuri-Wilson inequality
for polynomial semi-lattices.
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