Equal Entries in Totally Positive Matrices
Farber, Miriam · Faulk, Mitchell · Johnson, Charles R. · Marzion, Evan
Original · EN
We show that the maximal number of equal entries in a totally positive (resp. totally nonsingular) n-by-n matrix is Θ(n⁴/³) (resp. Θ(n³/²)). Relationships with point-line incidences in the plane, Bruhat order of permutations, and TP completability are also presented. We also examine the number and positionings of equal 2-by-2 minors in a 2-by-n TP matrix, and give a relationship between the location of equal 2-by-2 minors and outerplanar graphs.
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