L. Mutafchiev

activity

20062025

collaborators

11 papers

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 $σ = (σ_{1}, σ_{2}, \dots, σ_{n}) \in S_{n}$ . The {\it initial longest increasing sequence} (ILIS) in $σ$ has length $m$ i…

math.CO2023

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…

math.CO2022

The asymptotic of the number of permutations whose cycle lengths are prime numbers

Ljuben Mutafchiev

Let $A$ be a set of natural numbers and let $S_{n, A}$ be the set of all permutations of $[n] = {1, 2, ..., n}$ with cycle lengths belonging to $A$ . Furthermore, let $∣ A (n) ∣$ de…

math.CO2021

A Note on the Number of Permutations whose Cycle Lengths Are Prime Numbers

Ljuben Mutafchiev

Let $A$ be a set of natural numbers and let $S_{n, A}$ be the set of all permutations of $[n] = {1, 2, ..., n}$ with cycle lengths belonging to $A$ . For $A (n) = A \cap [n]$ , the limit $ρ=…

math.CO2020

Large Parts of Random Plane Partitions: a Poisson Limit Theorem

Ljuben Mutafchiev

We propose an aproach for asymptotic analysis of plane partition statistics related to counts of parts whose sizes exceed a certain suitably chosen level. In our study, we use the…