2 citations · 4 across the 9 of their papers we have counts for
12 papers
Quantum-Based Resilient Routing in Networks: Minimizing Latency Under Dual-Link Failures
Maher Harb, Nader Foroughi, Matt Stehman +3
Network optimization problems represent large combinatorial search spaces that grow exponentially with network size, making them computationally intensive to solve. This paper addr…
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…
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,…
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…
Matroids arising from electrical networks
Bob Lutz
This paper introduces Dirichlet matroids, a generalization of graphic matroids arising from electrical networks. We present four main theorems. First, we exhibit a matroid quotient…
Electrical networks and hyperplane arrangements
Bob Lutz
This paper studies \emph{Dirichlet arrangements}, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. We gene…
Graphical cyclic supercharacters for composite moduli
Bob Lutz
Recent work has introduced the study of graphical properties of cyclic supercharacters, functions whose values are exponential sums with clos…
Gauss' hidden menagerie: from cyclotomy to supercharacters
Stephan Ramon Garcia, Trevor Hyde, Bob Lutz
Gaussian periods, when viewed appropriately, exhibit a dazzling and eclectic host of visual qualities. This brief survey reviews the historical context and summarizes our current k…
Four quotient set gems
Bryan Brown, Michael Dairyko, Stephan Ramon Garcia +2
Our aim in this note is to present four remarkable facts about quotient sets. These observations seem to have been overlooked by the Monthly, despite its intense coverage of quotie…
A supercharacter approach to Heilbronn sums
Stephan Ramon Garcia, Bob Lutz
Various algebraic properties of Heilbronn's exponential sum can be deduced through the use of supercharacter theory, a novel extension of classical character theory due to Diaconis…
The graphic nature of Gaussian periods
William Duke, Stephan Ramon Garcia, Bob Lutz
Recent work has shown that the study of supercharacters on abelian groups provides a natural framework within which to study certain exponential sums of interest in number theory.…
Two remarks about nilpotent operators of order two
Stephan Ramon Garcia, Bob Lutz, Dan Timotin
We present two novel results about Hilbert space operators which are nilpotent of order two. First, we prove that such operators are indestructible complex symmetric operators, in…