Introduces the three-cosystole invariant for matroids and proves its optimal upper bound among regular matroids of rank at most six via monotonicity under extensions and explicit estimates on maximal simple examples.
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Establishes geodesic connectedness from completeness for affine connections on statistical manifolds with divisible cubic forms, producing a Cartan-Hadamard theorem.
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Higher cosystoles of matroids
Introduces the three-cosystole invariant for matroids and proves its optimal upper bound among regular matroids of rank at most six via monotonicity under extensions and explicit estimates on maximal simple examples.
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Geodesic Connectedness on Statistical Manifolds with Divisible Cubic Forms
Establishes geodesic connectedness from completeness for affine connections on statistical manifolds with divisible cubic forms, producing a Cartan-Hadamard theorem.