Ph.D
Group : Graphs, ALgorithms and Combinatorics

Combinatoire des fonctions de parking : Espèces, Énumération d’automates et Algèbres de Hopf

Starts on 01/10/2012
Advisor : HIVERT, Florent

Funding : Contrat doctoral uniquement recherche
Affiliation : Université Paris-Saclay
Laboratory :

Defended on 07/12/2015, committee :

Research activities :

Abstract :
This thesis comes within the scope of algebraic, bijective and enumerative combinatorics. It deals with the study of generalized parking functions following those axes.

In the first part, we are interested in generalized parking as a species of combinatorial structures (theory introduced by A. Joyal and developed by F. Bergeron, G. Labelle et P. Leroux). We define this species from a functional equation involving the species of set sequences. We lift the cycle index series to the non-commutative symmetric functions, expressed in several bases. By specialization, we obtain new enumeration formula for generalized parking and its isomorphism types.

By replacing the species of sets by others species in the functional equation, one defines new structures : the χ-parking tables. In particular cases with chi : m

CAUSAL LEARNING FOR DIAGNOSTIC SUPPORT


CAUSAL UNCERTAINTY QUANTIFICATION UNDER PARTIAL KNOWLEDGE AND LOW DATA REGIMES


MICRO VISUALIZATIONS: DESIGN AND ANALYSIS OF VISUALIZATIONS FOR SMALL DISPLAY SPACES
The topic of this habilitation is the study of very small data visualizations, micro visualizations, in display contexts that can only dedicate minimal rendering space for data representations. For several years, together with my collaborators, I have been studying human perception, interaction, and analysis with micro visualizations in multiple contexts. In this document I bring together three of my research streams related to micro visualizations: data glyphs, where my joint research focused on studying the perception of small-multiple micro visualizations, word-scale visualizations, where my joint research focused on small visualizations embedded in text-documents, and small mobile data visualizations for smartwatches or fitness trackers. I consider these types of small visualizations together under the umbrella term ``micro visualizations.'' Micro visualizations are useful in multiple visualization contexts and I have been working towards a better understanding of the complexities involved in designing and using micro visualizations. Here, I define the term micro visualization, summarize my own and other past research and design guidelines and outline several design spaces for different types of micro visualizations based on some of the work I was involved in since my PhD.