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".
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