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- W2201186759 abstract "We generalize the concept of ascending runs from permutations to Cayley trees and mappings. A combinatorial decomposition of the corresponding functional digraph allows us to obtain exact enumeration formulae that show an interesting connection to the Stirling numbers of the second kind. Using a bijective proof of Cayley's formula, we can show why the numbers of trees with a given number of ascending runs are directly linked to the corresponding numbers for mappings. Moreover, analytic tools allow a characterization of the limiting distribution of the random variable counting the number of ascending runs in a random mapping. As for permutations, this is a normal distribution with linear mean and variance." @default.
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- W2201186759 date "2015-07-20" @default.
- W2201186759 modified "2023-10-03" @default.
- W2201186759 title "Ascending Runs in Cayley Trees and Mappings" @default.
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