Rota’s basis conjecture
Given n bases of an n-dimensional space, can their vectors always be rearranged into n new bases, each taking one vector from every original base?
Bases and transversals
Rearranging bases, choosing distinct symbols and listing minimal hitting sets.
Subjects: Combinatorics · Algebra and geometry · Algorithms and data structures
Problems in this collection
4 problemsRyser’s Latin square conjecture
Does every odd-order Latin square have a transversal?
Hypergraph dualization
Can a classical polynomial-time algorithm recognize all minimal hitting sets?
Ryser’s hypergraph conjecture
Does every finite multipartite uniform hypergraph have a vertex cover at most r−1 times its largest matching?