We have made conjectures for the following objects, among others.
- Upper and lower bounds for the independence number of a graph.
- Upper and lower bounds for the determinant of a matrix.
- Necessary and sufficient conditions for whether a graph contains a hamilton cycle.
- Upper and lower bounds for various invariants associated with the game Chomp.
- Lower bounds for Goldbach(x), the number of ways to represent x as a sum of primes.