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math.CO2025
Matroid adjoints and the minimum rank of zero-nonzero matrix patterns
Louis Deaett, Kevin Grace
The problem of finding the minimum rank of a matrix with a given zero-nonzero pattern has been generalized to a class of matroids associated to the pattern. The fundamental lower b…
math.CO2025
The minors of matroids with an adjoint
Kevin Grace
If is a matroid, then a simple matroid with the same rank as is an adjoint of if there is an inclusion-reversing embedding of the lattice of flats of into…