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

Job advertisement - Research Assistant (3 years)

Fig.1 - Random realizations of all acyclic, realizable, non-degenerate, rank-2 chirotopes of size four.
The key objectives of this project are to: - Develop algorithms and algebraic structures to efficiently count permutation and higher-dimensional chirotope patterns. Identify subclasses of patterns that can be counted efficiently. - Develop a notion of entropy based on chirotope patterns to analyze the complexity of multidimensional time series. - Introduce cumulants of permutation and chirotope patterns and study their properties and applications in statistics. - Establish connections between counting patterns, dynamic programming, multiparameter integrals and (crossed modules of) Hopf algebras. Parts of the project are in collaboration with Kurusch Ebrahimi-Fard and Chaim Even-Zohar. The project is funded by the German Research Foundation (DFG) and runs from 2024 to 2027. It is part of the DFG priority programme SPP 2458 "Combinatorial Synergies". home