Containments in families with forbidden subposets

2021/08/23 by Dániel Nagy, Balázs Patkós, Nagy, Dániel +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.2108.10301

merged with arXiv:2108.08898

arxiv created 2021/11/16 · arxiv updated 2021/11/17

Abstract

We consider the problem of determining the maximum number of pairs F⊆ F' in a family F⊆ 2^[n] that avoids certain posets P of height 2. We show that for any such P the number of pairs is O(n\binomn\lfloor n/2\rfloor) and we find the exact value for the butterfly poset and the N poset. Also, we determine the asymptotics of the maximum number of pairs in containment for some posets of which the Hasse diagram is a path.

Citations

• On generalized Turán results in height two posets

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