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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
Relationships between minimum rank problem parameters for cobipartite graphs
Louis Deaett, Derek Young
For a simple graph, the minimum rank problem is to determine the smallest rank among the symmetric matrices whose off-diagonal nonzero entries occur in positions corresponding to t…