MathDBThe obstruction-containment conjecture relating TP and TN completion
The obstruction-containment conjecture relating TP and TN completion
A TP obstruction is a pattern that is not TP-completable, and a TN obstruction is a pattern that is not TN-completable. A pattern contains a pattern if occurs as a subpattern of in the obstruction sense used by the paper.
TP-to-TN obstruction conjecture. All TP obstructions contain a TN obstruction.
The paper proves this containment for all one-variable TP obstructions. The general relationship between TP and TN obstructions remains open; equivalently, the conjecture says that every TN-completable pattern is TP-completable.
Sources & referencesView supporting material
Primary source
Daniel Carter and Charles Johnson, “An Atomic Viewpoint of the TP Completion Problem”, arXiv:2203.04484 (2022).
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.