Enumerative and asymptotic combinatorics of discrete objects

Provider

Ministry of Education, Youth and Sports

Programme

Programme for Funding Multilateral Scientific and Technological Cooperation Projects in the Danube Region

Call for proposals

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Main participants

Univerzita Karlova / Matematicko-fyzikální fakulta

Contest type

M2 - International cooperation

Contract ID

-

Project name in Czech

Enumerative and asymptotic combinatorics of discrete objects

Annotation in Czech

This research proposal belongs to the field of Analytic Combinatorics, which combines methods from complex analysis, combinatorics, and probability theory to study the large-scale behaviour of discrete objects. We will focus on trees and tree-like structures, like maps and directed acyclic graphs. These objects are studied not only in mathematics, but naturally appear also in computer science, physics, chemistry, and even as remote fields as biology. The raised questions are as diverse as the different fields. We will focus on enumerative and asymptotic properties, meaning that we want to count the objects and understand their large-scale behaviour. Our goal is to understand the properties of a typical large representative. Here, a “typical” object is one chosen uniformly at random among all objects of fixed size. Therefore, the first step is to count the objects, like the number of trees with a given number of nodes. This then allows us in the second step to analyse certain parameters, like the depth, root degree, by enriching the counting sequence by these parameters. For these purposes, many new methods have been developed. Our general goal is to further develop these techniques and make the tools available to even more researchers. This project has the following goals: 1. characterizing the asymptotics of a class of bivariate recurrences with applications to permutations and maps; 2. studying functional equations for bivariate functions (enumerating size and some statistics, like pattern occurrences); 3. deriving limit laws related to extremal parameters.

R&D category

ZV - Basic research

OECD FORD - main branch

10101 - Pure mathematics

OECD FORD - secondary branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

OECD FORD - another secondary branch

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CEP - equivalent branches <br>(according to the <a href="http://www.vyzkum.cz/storage/att/E6EF7938F0E854BAE520AC119FB22E8D/Prevodnik_oboru_Frascati.pdf">converter</a>)

AF - Documentation, librarianship, work with information<br>BA - General mathematics<br>BC - Theory and management systems<br>BD - Information theory<br>IN - Informatics

Realization period - beginning

Jul 1, 2025

Realization period - end

Jun 30, 2027

Project status

Z - Beginning multi-year project

Latest support payment

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Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data delivery code

CEP25-MSM-8X-R

Data delivery date

Aug 6, 2025

Total approved costs

249 thou. CZK

Public financial support

249 thou. CZK

Other public sources

0 thou. CZK

Non public and foreign sources

0 thou. CZK