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Some greedyt-intersecting families of finite sequences

Some greedyt-intersecting families of finite sequences 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Some greedyt-intersecting families of finite sequences

Acta Mathematicae Applicatae Sinica , Volume 12 (4) – Jul 16, 2005

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Publisher
Springer Journals
Copyright
Copyright © 1996 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02029065
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 16, 2005

References