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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

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Enumerating all Hamiltonian Cycles in a Bipartite Vertex Transitive Graph

The case n=7 is pretty similar to counting the Hamiltonian cycles in the 6-cube (which has 64 vertices but more edges). That problem has been open for a long time, but was recently settled by Harri Ha …
Patric Ostergard's user avatar