Answering two OPAC problems involving Banff quivers
Tucker J. Ervin, Blake Jackson
Source abstract
In a post on the Open Problems in Algebraic Combinatorics (OPAC) blog, E. Bucher and J. Machacek posed three open problems: OPAC-033, OPAC-034, and OPAC-035. These three problems deal with the relationships between three infinite classes of quivers: the Banff, Louise, and 𝒫 quivers. OPAC-034 asks whether or not every Banff quiver can be verified to be Banff by only considering sources and sinks, and OPAC-035 asks whether or not every Banff quiver is contained in the class 𝒫 . We answer both questions in the affirmative, showing that every Banff quiver can be verified to be Banff by using sources and sinks, and therefore that every Banff quiver lives in the class 𝒫 . We also make some progress on OPAC-033, showing a result similar to our result OPAC-034 for Louise quivers.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.