67 citations · 180 across the 16 of their papers we have counts for
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math.CO2019★ 1 cited
Dimension is polynomial in height for posets with planar cover graphs
Jakub Kozik, Piotr Micek, William T. Trotter
We show that height posets that have planar cover graphs have dimension . Previously, the best upper bound was . Planarity plays a key r…
math.CO2019
Planar Posets that are Accessible from Below Have Dimension at Most 6
Csaba Biró, Bartłomiej Bosek, Heather C. Smith +3
Planar posets can have arbitrarily large dimension. However, a planar poset of height has dimension at most , while a planar poset with minimal elements has dimens…
math.CO2019
Fractional Local Dimension
Heather C. Smith, William T. Trotter
The original notion of dimension for posets was introduced by Dushnik and Miller in 1941 and has been studied extensively in the literature. In 1992, Brightwell and Scheinerman dev…