Distribution of ascents, descents, and plateaus

Determine the distributions of ascents, descents, and plateaus in frustrated parking functions.

Background

The paper develops enumerative results for frustrated parking functions, including counts by the number of lucky cars and spots, but does not determine the joint or individual distributions of the standard word statistics of ascents, descents, and plateaus. The authors identify these distributions as unresolved questions, by analogy with corresponding questions for classical parking functions.

References

What does the distribution of descent/ascents/plateaus in frustrated parking functions look like?

— Parking with Frustrated Drivers  (2609.35638 - Hallam et al., 28 Sep 2026) in Section 'Open Questions', Question following the introductory paragraph on ascents, descents, and plateaus