Projects

I work in extremal and enumerative combinatorics, with applications to theoretical computer science. My projects include:

• Extremal Combinatorics
• Enumerative Combinatorics

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Extremal Combinatorics

• (with Zachary Hammersla and Kevin Milans) Ramsey Numbers of Matchings in Ordered Graphs (in preparation)

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Enumerative Combinatorics

• (with Levi Axelrod, Nathan Bickel, Anastasia Halfpap, Alex Parker, and Cole Swain) Statistics of Maximal Independent Sets in Grid-Like Graphs, preprint (2025), 24 pages.

  An independent set \( I \) in a graph \( G \) is maximal if \( I \) is not properly contained in any other independent set of \( G \). One class of graphs where enumeration of MIS’s is well-understood is the rectangular grid graphs \( G_{m \times n} \). We study properties of MIS’s in "grid-like" graphs — graphs locally isomorphic to square grids but globally resembling surfaces like tori or Möbius strips.

  We examine parity, average size, and number of non-isomorphic MIS's in various families of grid-like graphs.

  See our preprint on Arxiv.
  See our poster presented at JMM 2025 in Seattle, WA.
  Also see slides.

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