TP_k Completion of Patterns with One Unspecified Entry
Electronic Journal of Linear Algebra
Totally positive-k matrix, Completion problem, Pattern, Polynomial conditions
Every partial TP2 (TP1) matrix with one unspecified entry has a TP2 (TP1) completion. For a given m-by-n pattern with one unspecified entry, the minimum set of conditions characterizing TP3 completability is given. These conditions are at most eight polynomial inequalities on the specified entries of the pattern. For k ≥ 3, patterns with one unspecified entry that are TPk completable are also characterized, and conditions are described for completability otherwise
Akin, V.; Johnson, C. R.; and Nasserasr, Shahla, "TP_k Completion of Patterns with One Unspecified Entry" (2014). Mathematics Faculty Articles. 129.