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math.AC2021
When are symmetric ideals monomial?
Andreas Kretschmer
We study conditions on polynomials such that the ideal generated by their orbits under the symmetric group action becomes a monomial ideal or has a monomial radical. If the polynom…
math.ST2021★ 3 cited
The geometry of Gaussian double Markovian distributions
Tobias Boege, Thomas Kahle, Andreas Kretschmer +1
Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs specifying zeros simultaneously in the covariance matrix and its inverse. We study t…
math.AG2021
Liftings of polynomial systems decreasing the mixed volume
Christopher Borger, Thomas Kahle, Andreas Kretschmer +2
The BKK theorem states that the mixed volume of the Newton polytopes of a system of polynomial equations upper bounds the number of isolated torus solutions of the system. Homotopy…