Burnside processes on parking functions and Dyck paths mix in O(n log n) time, yielding approximate uniform sampling algorithms for increasing parking functions, Dyck paths, and polygon triangulations.
Dittmer,Counting linear extensions and contingency tables, PhD Thesis, University of California Los Angeles, ProQuest LLC, (2019)
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Burnside process on parking functions and Dyck paths
Burnside processes on parking functions and Dyck paths mix in O(n log n) time, yielding approximate uniform sampling algorithms for increasing parking functions, Dyck paths, and polygon triangulations.