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-nTP matrix, and give a relationship between the location of
equal 2-by-2 minors and outerplanar graphs.Comment: 15 page