3 papers
math.CO2020
Local -dimension
David Lewis
In this note, we introduce a new poset parameter called local -dimension. We also discuss the fractional variants of this and other dimension-like parameters.
math.CO2020
On Covering Numbers, Young Diagrams, and the Local Dimension of Posets
Gábor Damásdi, Stefan Felsner, António Girão +4
We study covering numbers and local covering numbers with respect to difference graphs and complete bipartite graphs. In particular we show that in every cover of a Young diagram w…
math.CO2020
The local dimension of suborders of the Boolean lattice
David Lewis
We prove upper and lower bounds on the local dimension of any pair of layers of the Boolean lattice, and show that the local dimension of the first and middle layers of the -dim…