Families of Subsets Without a Given Poset in Double Chains and Boolean Lattices

Jun Yi Guo, Fei Huang Chang, Hong Bin Chen, Wei Tian Li*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

摘要

Given a finite poset P, the intensively studied quantity La(n, P) denotes the largest size of a family of subsets of [n] not containing P as a weak subposet. Burcsi and Nagy (J. Graph Theory Appl. 1, 40–49 2013) proposed a double-chain method to get an upper bound La(n,P)≤12(|P|+h−2)(n⌊n/2⌋) for any finite poset P of height h. This paper elaborates their double-chain method to obtain a new upper boundLa(n,P)≤(|P|+h−α(GP)−22)(n⌊n2⌋)for any graded poset P, where α(GP) denotes the independence number of an auxiliary graph defined in terms of P. This result enables us to find more posets which verify an important conjecture by Griggs and Lu (J. Comb. Theory (Ser. A) 119, 310–322, 2012).

原文英語
頁(從 - 到)349-362
頁數14
期刊Order
35
發行號2
DOIs
出版狀態已發佈 - 2018 七月 1

ASJC Scopus subject areas

  • 代數與數理論
  • 幾何和拓撲
  • 計算機理論與數學

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