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Award ID contains: 1839406

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  1. (, The Electronic Journal of Combinatorics)
    We demonstrate a method for proving precise concentration inequalities in uniformly random trees on $$n$$ vertices, where $$n\geq1$$ is a fixed positive integer. The method uses a bijection between mappings $$f\colon\{1,\ldots,n\}\to\{1,\ldots,n\}$$ and doubly rooted trees on $$n$$ vertices. The main application is a concentration inequality for the number of vertices connected to an independent set in a uniformly random tree, which is then used to prove partial unimodality of its independent set sequence. So, we give probabilistic arguments for inequalities that often use combinatorial arguments. 
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  2. (, Notices of the American Mathematical Society)
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