A Note on the Largest Size of Families of Sets with a Forbidden Poset

Hong-Bin Chen; Wei-Tian Li

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A Note on the Largest Size of Families of Sets with a Forbidden Poset

机译：关于带有禁止词组的最大集合族的注记

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摘要

Consider families of subsets of [n] := {1, 2.....n) that do no contain a given poset P as a subposet. Let La(n, P) denote the largest size of such families and h(P) denote the height of P. The best known general upper bound for La(n, P) is (1/2 (|P| + h(P)) - 1) (n [n/2]), due to Bursi and Nagy (2012). This paper provides an improved upper bound 1/(m+1) (|P| + 1/2(m~2 + 3m - 2)(h( P) -1) - 1) (n [n/2]), where m can be any positive integer less than [n/2].

机译：考虑[n]：= {1，2 ..... n）的子集族，这些子集不包含给定的位姿P作为子位姿。令La（n，P）表示此类族的最大大小，h（P）表示P的高度。La（n，P）的最著名的一般上限为（1/2（| P | + h（ P））-1）（n [n / 2]），归因于Bursi和Nagy（2012）。本文提供了一种改进的上限1 /（m + 1）（| P | + 1/2（m〜2 + 3m-2）（h（P）-1）-1）（n [n / 2]），其中m可以是小于[n / 2]的任何正整数。

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来源
《Order》 |2014年第1期|137-142|共6页
作者
Hong-Bin Chen; Wei-Tian Li;
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作者单位

Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan;

Department of Applied Mathematics, National Chung Hsing University, Taichung 40227, Taiwan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Families of subsets; Forbidden subposets; Double counting;

机译：子集家族;禁止的子代;重复计算;

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A Note on the Largest Size of Families of Sets with a Forbidden Poset

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