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University of San Francisco

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Representative Papers

Connectivity of Districting Metagraphs

Jun 08, 2026

This study investigates the irreducibility of ReCom-based Markov chains in political redistricting to ensure representative sampling of districting plans. Employing tools from graph theory and Markov chain Monte Carlo methods, the authors establish—for the first time—the irreducibility of the two-partition ReCom chain on subgraphs of the triangular lattice and prove irreducibility for three-equal-partition ReCom chains on 3×n grid graphs. Conversely, they construct an infinite family of counterexamples demonstrating that even minor structural variations in closely related planar subdivisions can render the chain disconnected, highlighting the fragility of irreducibility. These results delineate critical theoretical boundaries for assessing fairness in redistricting algorithms.

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Latest Papers

Connectivity of Districting Metagraphs

Jun 08, 2026

This study investigates the irreducibility of ReCom-based Markov chains in political redistricting to ensure representative sampling of districting plans. Employing tools from graph theory and Markov chain Monte Carlo methods, the authors establish—for the first time—the irreducibility of the two-partition ReCom chain on subgraphs of the triangular lattice and prove irreducibility for three-equal-partition ReCom chains on 3×n grid graphs. Conversely, they construct an infinite family of counterexamples demonstrating that even minor structural variations in closely related planar subdivisions can render the chain disconnected, highlighting the fragility of irreducibility. These results delineate critical theoretical boundaries for assessing fairness in redistricting algorithms.

0 citationsRead paper