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math.CO2023
Plücker inequalities for weakly separated coordinates in totally nonnegative Grassmannian
Daniel Soskin, Prateek Kumar Vishwakarma
We show that the partial sums of the long Plücker relations for pairs of weakly separated Plücker coordinates oscillate around on the totally nonnegative part of the Grassmanni…
math.CA2023★ 1 cited
Inequalities for totally nonnegative matrices: Gantmacher--Krein, Karlin, and Laplace
Shaun M. Fallat, Prateek Kumar Vishwakarma
A real linear combination of products of minors which is nonnegative over all totally nonnegative (TN) matrices is called a determinantal inequality for these matrices. It is refer…
math.CO2023
The Strong Spectral Property of Graphs: Graph Operations and Barbell Partitions
Sarah Allred, Emelie Curl, Shaun Fallat +4
The utility of a matrix satisfying the Strong Spectral Property has been well established particularly in connection with the inverse eigenvalue problem for graphs. More recently t…