Abstract
Abstract The 3-by-n TP-completable patterns are characterized by identifying the minimal obstructions up to natural symmetries. They are finite in number.
Highlights
An m × n real matrix A is called totally positive (TP) if each of its minors is positive
A partial matrix is a rectangular array in which some entries are speci ed and the remaining, unspeci ed entries are free to be chosen
A completion of a partial matrix is a choice of values for the unspeci ed entries, resulting in a conventional matrix
Summary
An m × n real matrix A is called totally positive (TP) if each of its minors (determinants of square submatrices) is positive. We have a partial TP matrix with 2 unspeci ed entries in the same column, which is TP-completable by Theorem 2. Let A be a partial TP matrix of pattern P, and complete the entries in columns 1 through i + and in columns i through n using the completability of P and P respectively.
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