Some greedyt-intersecting families of finite sequences期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Some greedyt-intersecting families of finite sequences

Authors:	Shiquan WU

Affiliation:	(1) Department of Mathematics, National University of Technology, 410073 Changsha, China

Abstract:	Letn, s₁,s₂, ... 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, denotes_p(a)={j\|1jn,a_jp}, $S_p (mathcal{F}) = { s_p (a)\|a in mathcal{F}}$ , and $W_p (A) = p^{n - \|A\|} prodlimits_{i in A} {(s_i - p)}$ . is called anI_t^p-intersecting family if, for any a,b,a_ib_i=min(a_i,b_i)p for at leastt i's. is called a greedyI_t^P-intersecting family if is anI_t^p-intersecting family andW_p(A)W_p (B+A^c) for anyAS_p() and any with \|B\|=t–1.In this paper, we obtain a sharp upper bound of \|\| for greedyI_t^p-intersecting families in $mathcal{M}(s_1 ,s_2 , cdots ,s_n )$ for the case 2ps_i (1in) ands₁>s₂>...>s_n.This project is partially supported by the National Natural Science Foundation of China (No.19401008) and by Postdoctoral Science Foundation of China.

Keywords:	I_t^p-greedy subsets I_t^p-regular subset t-intersecting family I^p_t-intersecting family greedyI_t^p-intersecting family
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