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math.CO2020
Discrete homotopy of token configurations
Bob Lutz
This paper studies graphical analogs of symmetric products and unordered configuration spaces in topology. We do so from the perspective of the discrete homotopy theory introduced…
math.CO2020
Higher discrete homotopy groups of graphs
Bob Lutz
This paper studies a discrete homotopy theory for graphs introduced by Barcelo et al. We prove two main results. First we show that if is a graph containing no 3- or 4-cycles,…
math.CO2018
Koszulness and supersolvability for Dirichlet arrangements
Bob Lutz
We prove that the cone over a Dirichlet arrangement is supersolvable if and only if its Orlik-Solomon algebra is Koszul. This was previously shown for four other classes of arrange…