Strongly maximal antichains in posets

Ron Aharoni, Eli Berger

Research output: Contribution to journalArticlepeer-review


Given a collection S of sets, a set S∈S is said to be strongly maximal in S if T\S|≤|S\T| for every T∈S. In Aharoni (1991) [3] it was shown that a poset with no infinite chain must contain a strongly maximal antichain. In this paper we show that for countable posets it suffices to demand that the poset does not contain a copy of posets of two types: a binary tree (going up or down) or a "pyramid". The latter is a poset consisting of disjoint antichains Ai,i=1,2,..., such that |Ai|=i and x<y whenever x∈Ai,y∈Aj and j<i (a "downward" pyramid), or x<y whenever x∈Ai, y∈Aj and i<j (an "upward" pyramid).

Original languageEnglish
Pages (from-to)1518-1522
Number of pages5
JournalDiscrete Mathematics
Issue number15
StatePublished - 6 Aug 2011


  • Antichains
  • Posets
  • Strongly maximal
  • Waves

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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