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

• Applicant: Professor Dr. Joscha Diehl
• 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
• Subproject of: SPP 2458: Combinatorial Synergies
• International Connection: Israel, Norway
• Cooperation Partners: Professor Dr. Kurusch Ebrahimi-Fard; Professor Dr. Chaim Even-Zohar