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




  chirotopes
  
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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