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Python-script for computing the values of small diagrams in the Gaudin-Gilespie-Ripka (GGR) expansion.

The GGR expansion is explained in the papers:

  • Almost optimal upper bound for the ground state energy of a dilute Fermi gas via cluster expansion
    A. B. Lauritsen, arXiv:2301.08005

  • Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion
    A. B. Lauritsen and R. Seiringer, arXiv:2301.04894

The script takes as input a graph and outputs all equivalence classes of quasi-linked permutations, meaning permutations with each linked component having at least one external vertex.

Two permutations/diagrams are equivalent if they have the same value. This happens if the permutations are related by a symmetry of the graph. For each equivalence class is computed the weight being the sign times the number of equivalent permutations in the equivalence class.

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Python-script for calculating values of GGR-diagrams

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