A matrix is called totally nonnegative (TN) if the determinant of every square submatrix is nonnegative and totally positive (TP) if the determinant of every square submatrix is positive. The TP (TN) completion problem asks which partial matrices have a TP (TN) completion. In this paper, a new class of TP- and TN- completable patterns, the border patterns, is identified. This answers an unpublished question about TP-completable patterns that has been outstanding for some time and is the first case of completable patterns with all entries on the border specified. In the process, a new tool is developed: TP line insertion in the second or penultimate line when the first and last entries of the line are specified. Prior results about single un...
A pattern is a list of positions in an n×n real matrix. A matrix completion problem for the class of...
A matrix is called TP2 if all 1-by-1 and 2-by-2 minors are positive. A partial matrix is one with so...
Abstract For a class X of real matrices, a list of positions in an n × n matrix (a pattern) is said ...
A matrix is called totally nonnegative (TN) if the determinant of every square submatrix is nonnegat...
Though some special cases are now understood, the characterization of TP-completable patterns is far...
We first give a complete list of polynomial conditions on the data for TP (TN) completability of par...
Abstract. Every partial TP2 (TP1) matrix with one unspecified entry has a TP2 (TP1) com-pletion. For...
Every partial TP2 (TP1) matrix with one unspecified entry has a TP2 (TP1) completion. For a given m-...
We present two complementary techniques called catalysis and inhibition which allow one to determine...
The 3-by-n TP-completable patterns are characterized by identifying the minimal obstructions up to n...
The notions of total positivity and of TPk are generalized to shapes (a generalization of matrices...
AbstractThe notions of total positivity and of TPk are generalized to “shapes” (a generalization of ...
Here, we define and consider (linear) TP-directions and TP-paths for a totally nonnegative matrix, i...
In earlier work, the labelled graphs G for which every combinatorially symmetric totally nonnegative...
An n-by-n real matrix is said to be totally positive (nonnegative) if every minor (principal and non...
A pattern is a list of positions in an n×n real matrix. A matrix completion problem for the class of...
A matrix is called TP2 if all 1-by-1 and 2-by-2 minors are positive. A partial matrix is one with so...
Abstract For a class X of real matrices, a list of positions in an n × n matrix (a pattern) is said ...
A matrix is called totally nonnegative (TN) if the determinant of every square submatrix is nonnegat...
Though some special cases are now understood, the characterization of TP-completable patterns is far...
We first give a complete list of polynomial conditions on the data for TP (TN) completability of par...
Abstract. Every partial TP2 (TP1) matrix with one unspecified entry has a TP2 (TP1) com-pletion. For...
Every partial TP2 (TP1) matrix with one unspecified entry has a TP2 (TP1) completion. For a given m-...
We present two complementary techniques called catalysis and inhibition which allow one to determine...
The 3-by-n TP-completable patterns are characterized by identifying the minimal obstructions up to n...
The notions of total positivity and of TPk are generalized to shapes (a generalization of matrices...
AbstractThe notions of total positivity and of TPk are generalized to “shapes” (a generalization of ...
Here, we define and consider (linear) TP-directions and TP-paths for a totally nonnegative matrix, i...
In earlier work, the labelled graphs G for which every combinatorially symmetric totally nonnegative...
An n-by-n real matrix is said to be totally positive (nonnegative) if every minor (principal and non...
A pattern is a list of positions in an n×n real matrix. A matrix completion problem for the class of...
A matrix is called TP2 if all 1-by-1 and 2-by-2 minors are positive. A partial matrix is one with so...
Abstract For a class X of real matrices, a list of positions in an n × n matrix (a pattern) is said ...
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