Caleb Stanford


Projects

  • Capstone project at Brown (spring 2016)

    My undergraduate capstone project at Brown was on verifying the solutions to several epistemic logic puzzles in the Alloy programming language. The abstract is here. You can also download the Alloy files and run them yourself; they are here.

  • Undergraduate Research (summer 2015)

    I attended the Complexity Across Disciplines Math REU in summer 2015. The work was in graph theory and combinatorics. We studied a particular operation, called a ‘context-directed reversal’, on signed permutations — permutations of where each element is additionally given a sign.

    The main result classifies exactly which signed permutations are sortable by context-directed reversals. We are unable to provide a formula for the number of such signed permutations, but we relate signed permutations to a subclass of graphs, and provide a formula for the number of graphs sortable by an analogous graph operation. We prove that asymptotically it is 1/3 of all graphs.

    Here are some slides on our work and a final poster which we presented at the Joint Math Meetings (JMM) in January 2016, winning an Outstanding Presentation Award.

Exposition



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