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Letn, s 1,s 2, ... ands n be positive integers. Assume $$\mathcal{M}(s_1 ,s_2 , \cdots ,s_n ) = \{ (x_1 ,x_2 , \cdots x_n )|0 \leqslant x_i \leqslant s_i ,x_i$$ is an integer for eachi}. For $$a = (a_1 ,a_2 , \cdots a_n ) \in \mathcal{M}(s_1 ,s_2 , \cdots ,s_n )$$ , $$\mathcal{F} \subseteq \mathcal{M}(s_1 ,s_2 , \cdots ,s_n )$$ , and $$A \subseteq \{ 1,2, \cdots ,n\}$$ , denotes p (a)={j|1≤j≤n,a j ≥p}, $$S_p (\mathcal{F}) = \{ s_p (a)|a \in \mathcal{F}\}$$ , and $$W_p (A) = p^{n - |A|} \prod\limits_{i \in A} {(s_i - p)}$$ . $$\mathcal{F}$$ is called anI t p -intersecting family if, for any a,b∈ $$\mathcal{F}$$ ,a i Λb i =min(a i ,b i )≥p for at leastt i's. $$\mathcal{F}$$ is called a greedyI t P -intersecting family if $$\mathcal{F}$$ is anI t p -intersecting family andW p (A)≥W p (B+A c ) for anyAεS p ( $$\mathcal{F}$$ ) and any $$B \subseteq A$$ with |B|=t−1.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 16, 2005
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