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The Logarithmic Method And The Solution To The Tp2-Completion Problem, Shahla Nasserasr
The Logarithmic Method And The Solution To The Tp2-Completion Problem, Shahla Nasserasr
Dissertations, Theses, and Masters Projects
A matrix is called TP2 if all 1-by-1 and 2-by-2 minors are positive. A partial matrix is one with some of its entries specified, while the remaining, unspecified, entries are free to be chosen. A TP2-completion, of a partial matrix T , is a choice of values for the unspecified entries of T so that the resulting matrix is TP2. The TP2-completion problem asks which partial matrices have a TP2-completion. A complete solution is given here. It is shown that the Bruhat partial order on permutations is the inverse of a certain natural partial order induced by TP2 matrices and …