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math.CO2022
Partial shuffles by lazy swaps
Barnabás Janzer, J. Robert Johnson, Imre Leader
What is the smallest number of random transpositions (meaning that we swap given pairs of elements with given probabilities) that we can make on an -point set to ensure that eac…
math.CO2022
Optimal Resistor Networks
J. Robert Johnson, Mark Walters
Given a graph on n vertices with m edges, each of unit resistance, how small can the average resistance between pairs of vertices be? There are two very plausible extremal construc…