Improve the exponential lower bound for peeling sequences

Improve the lower bound for the minimum number of peeling sequences in an n-point planar set in general position from the currently known form g(n)\ge c\cdot 3^n, where c is a positive constant; in particular, establish whether a polynomial factor can be obtained.

Background

The paper studies g(n), the minimum number of peeling sequences over all n-point planar sets in general position. Every such set has at least three convex-hull vertices, yielding the recursive lower bound g(n)\ge 3g(n-1) and hence g(n)\ge 2\cdot 3^{n-2}, equivalently a bound of the form c\cdot 3^n for a positive constant c.

The paper’s main contribution is an improved upper bound obtained from a recursively defined three-block construction and directional restrictions. The concluding remarks identify the unresolved complementary direction: strengthening the relatively weak exponential lower bound. The authors specifically note that even obtaining a polynomial factor beyond the exponential term would be interesting.