# Random Combinatorial Structures

A special issue of *Mathematics* (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: **closed (30 September 2023)** | Viewed by 7859

## Special Issue Editors

**Interests:**theoretical and applied probability; random processes; statistics; modelling of extreme values; statistical physics; mathematical physics; probabilistic combinatorics

**Interests:**probability; random matrix theory; number theory; representation theory; function theory; combinatorics

**Interests:**probability limit theory with applications; random integer partitions; random matrix theory; percolation theory; random growth models

**Interests:**probability theory; stochastic processes; probabilistic combinatorics; integer partitions; finite set partitions; exchangeability

## Special Issue Information

Dear Colleagues,

Loosely speaking, decomposable combinatorial structures are characterized via their components, such as cycles in permutations, parts in integer partitions, connected components in graphs, irreducible factors in polynomials over finite fields, etc. Such structures are ubiquitous in numerous areas of mathematics and its applications—from number theory, algebra, and topology to quantum physics, statistics, population genetics, IT, and cryptography.

Modern approach to “big” combinatorial structures is concerned with their typical macroscopic properties (e.g., limit shape) under a suitable probability measure. Of particular interest are possible effects caused by various constraints imposed, say, on the source of components, their multiplicities, total number, etc. Possible multivariate extensions include convex lattice chains (polygonal lines) and zonotopes. Furthermore, many topics in related domains may have a similar flavor—for example, in random matrix theory, with interesting subclasses exemplified by permutation matrices and band matrices.

This Special Issue aims at collecting high-quality papers to summarize and consolidate the state of the art in this fascinating research area along with modern advances in diverse applications.

Dr. Leonid V. Bogachev

Dr. Dirk Zeindler

Prof. Dr. Zhonggen Su

Dr. Yuri V. Yakubovich*Guest Editors*

**Manuscript Submission Information**

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## Keywords

- decomposable combinatorial structures
- structural constraints
- random integer partitions
- finite set partitions
- random permutations
- spatial permutations
- multivariate extensions (e.g., convex lattice chains, digital polyominoes, polytopes, zonotopes)
- limit shapes
- asymptotic fluctuations
- generating functions
- random matrix theory
- applications (e.g., quantum physics, statistics, economics, population genetics, IT, cryptography)