L. Mutafchiev

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3 papers · 1 filter

math.CO2025

Large Components and Trees of Random Mappings

Ljuben Mutafchiev, Steven Finch

Let $T_{n}$ be the set of all mappings $T : [n] \to [n]$ , where $[n] = {1, 2, \dots, n}$ . The corresponding graph $G_{T}$ of $T$ , called a functional digraph, is a union of disjoin…

math.CO2025

A note on the distribution of the sum of lengths of the initial longest increasing sequences in cycles of random permutations

Ljuben Mutafchiev

Let $S_{n}$ be the set of all permutations of ${1, 2, \dots, n}$ and let $I ¨ = (I ¨ _{1}, I ¨ _{2}, \dots, I ¨ _{n}) \in S_{n}$ . The {\it initial longest increasing sequence} (ILIS) in $I ¨ $ has length…

math.CO2024

On the Deepest Cycle of a Random Mapping

Ljuben Mutafchiev, Steven Finch

Let $T_{n}$ be the set of all mappings $T : {1, 2, \dots, n} \to {1, 2, \dots, n}$ . The corresponding graph of $T$ is a union of disjoint connected unicyclic components. We ass…