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- W3092488660 abstract "Abstract An integer partition is called graphical if it is the degree sequence of a simple graph. We prove that the probability that a uniformly chosen partition of size $n$ is graphical decreases to zero faster than $n^{-.003}$, answering a question of Pittel. A lower bound of $n^{-1/2}$ was proven by Erd̋s and Richmond, meaning our work demonstrates that the probability decreases polynomially. Our proof also implies a polynomial upper bound for the probability that two randomly chosen partitions are comparable in the dominance order." @default.
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- W3092488660 date "2020-10-06" @default.
- W3092488660 modified "2023-10-16" @default.
- W3092488660 title "Asymptotic Bounds on Graphical Partitions and Partition Comparability" @default.
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- W3092488660 doi "https://doi.org/10.1093/imrn/rnaa251" @default.
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