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Edouard Heitzmann
    Hi! I’m Edouard Heitzmann, currently a Mathematics PhD student in Mathematics at the University of Colorado, Boulder, under the mentorship of Professor Jeanne Clelland . I study structural democracy with the Data and Democracy Lab; recently, we’ve been studying political redistricting and ranked choice voting systems. My mathematical specialization is in Markov Chains, Discrete Geometry, and Graph Theory.
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    • Probabilistically Counting the Districtings of a Graph

      Posted on 13 mins

      Given a planar graph \(G = (V,E)\) and district sizes \(\lbrace k_i\rbrace_{i=1}^n\), a political districting of \(G = (V,E)\) is a partition \(\lbrace P_i\rbrace_{i=1}^n\) of \(G\) into (simply-)connected subgraphs (called districts) satisfying \(|P_i|=k_i\).

      For the purposes of this project, I’ve usually taken \(G\) be an \(n\times n\) grid graph and \(k_i=n\) for all \(i\); but this was a choice made of convenience, not necessity. This project explores a method to stochastically estimate the number of districtings of \(G\) when enumerating them is not computationally viable.