English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This thesis deals with the enumerative study of combinatorial maps, and itsapplication to the enumeration of other combinatorial objects.  Combinatorial maps, or simply maps, form a rich combinatorial model. Theyhave an intuitive and geometric definition, but are also related to some deepalgebraic structures. For instance, a special type of maps calledconstellations provides a unifying framework for some enumeration problemsconcerning factorizations in the symmetric group. Standing on a position wheremany domains meet, maps can be studied using a large variety of methods, andtheir enumeration can also help us count other combinatorial objects. Thisthesis is a sampling from the rich results and connections in the enumerationof maps.  This thesis is structured into four major parts. The first part, includingChapter 1 and 2, consist of an introduction to the enumerative study of maps.The second part, Chapter 3 and 4, contains my work in the enumeration ofconstellations, which are a special type of maps that can serve as a unifyingmodel of some factorizations of the identity in the symmetric group. The thirdpart, composed by Chapter 5 and 6, shows my research on the enumerative linkfrom maps to other combinatorial objects, such as generalizations of the Tamarilattice and random graphs embeddable onto surfaces. The last part is theclosing chapter, in which the thesis concludes with some perspectives andfuture directions in the enumerative study of maps.

Enumerative and bijective aspects of combinatorial maps: generalization, unification and application (PhD thesis)