Exact selection complexities for ranks 6 through 9 with 17 elements

Determine the exact values of the minimum worst-case comparison counts V_6(17), V_7(17), V_8(17), and V_9(17) for selecting ranks 6 through 9 among 17 distinct elements.

Background

For 17 elements, the paper establishes V_5(17)=27 and gives upper bounds V_6(17)≤29, V_7(17)≤30, V_8(17)≤31, and V_9(17)≤31. Combined with the stated lower bounds, the unresolved ranges are 28–29, 29–30, 29–31, and 29–31, respectively. The authors explicitly identify these gaps as remaining open.

References

The gaps for $n=17$ at ranks 6--9 remain open.

— Selecting the 7th Smallest of 16 Elements Takes Exactly 28 Comparisons  (2610.18740 - Cremer, 13 Oct 2026) in Section “Conclusion and open problems,” paragraph “Open problems”