In reality: all of them.
In idealized bifurcation buckling for columns and unstiffened plates (eigenvalue analysis, elastic behavior): span (length of a column or lengths of sides of a plate), Young´s modulus, cross-sectional geometry (second moment of area in weak axis for beams, plate thickness and Poisson's ratio for plates), and boundary conditions. These four aspects are immediately obvious by inspection of e.g., the basic Euler buckling cases, which you should find in your textbook.