Project Details
Projekt Print View

Counting permutation and chirotope patterns: algorithms, algebra, and applications

Subject Area Mathematics
Term since 2024
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 539875438
 
The key objectives of this project are to: 1) Develop algorithms and algebraic structures to efficiently count permutation and higher-dimensional chirotope patterns. Identify subclasses of patterns that can be counted efficiently. 2) Initiate the study of chirotope patterns as a research topic, investigating classical permutation pattern topics like pattern avoidance in this new context. 3) Develop a notion of entropy based on chirotope patterns to analyze the complexity of multidimensional time series. 4) Introduce cumulants of permutation and chirotope patterns and study their properties and applications in combinatorics and statistics. 5) Establish connections between counting patterns, dynamic programming, multiparameter integrals, and (crossed modules of) Hopf algebras.
DFG Programme Priority Programmes
International Connection Israel, Norway
 
 

Additional Information

Textvergrößerung und Kontrastanpassung