Compare Antisymmetric and Symmetric OP: Edge Plots
We only compare bottom edges, because by symmetry, the side edge of the Symmetric OP is the same as the bottom edge. Similarly, by antisymmetry, the side edges of the Antisymmetric OP must have one boundary fixed at zero. The Antisymmetric OP are shown on the left, and the Symmetric OP are on the right.
Note that for both OP the number of zeros increase with degree. It seems that the Antisymmetric edges have exactly one more zero than do the Symmetric edges of the same degree. There is the exception of k=10, and it is difficult to tell for k≥14 because the oscillation seems to be on a finer scale than our resolution.
Both polynomials seem to show the "interweaving" behavior of the zeros. Conjecture that the zeros of Sk interweave with the zeros of Qk? Finally, both OP show clustering of the zeros near the endpoints.
