Explanation of the comb-like closeness histogram

Explain the comb-like histogram pattern observed for the convex-set closeness values between seven-element posets, including the apparent interlacing of two distributions with different means and amplitudes.

Background

The paper defines a closeness function by taking coefficientwise absolute differences between the convex-set generating polynomials of two posets. For pairs of seven-element posets, the resulting histogram exhibits a comb-like pattern that is absent from the analogous interval-based closeness histogram. The authors report that they do not yet understand the source of this behavior.

References

What we observe is a comb-like pattern to the histogram for the \mathcal{D}{convex} plot, where there are seemingly two distributions of differing means and amplitudes that interlace each other. This behaviour is not observed for \mathcal{D}{interval}. As of yet we do not have an explanation for this phenomenon, so it remains a combinatorial oddity.

— A Generating Polynomial for Convex Subsets of Posets  (2610.23399 - George et al., 16 Oct 2026) in Section 6.3, “Convex Sets in Causal Sets”