Kotesovec’s binomial-sum asymptotic conjecture
The conjecture asserts an asymptotic formula for a binomial sum arising in the enumeration of -Dyck paths and related enumeration problems. The supplied sources do not state the binomial sum or its conjectured asymptotic precisely enough to give a more exact formal statement.
References
Primary source
Additional references
- The Area Asymptotics of (sn,n)-Dyck Paths — arXiv — Evan Conway, James Harbour
Progress summary
A new preprint claims to confirm the conjecture, but the result has not yet received independent mathematical assessment.
The conjecture concerns the asymptotic behavior of a binomial sum arising from Fuss–Catalan Dyck-path enumeration. Its exact originator and date are not identified in the retrieved material.
October 2026 claimed confirmation
Evan Conway and James Harbour report an exact total-area formula for -Dyck paths and state that it confirms Kotesovec’s asymptotic conjecture, while also deriving average-area bounds. This is a claimed complete resolution in a new preprint and remains unverified.
Current status (as of October 2026): The conjecture is claimed confirmed by Conway and Harbour’s preprint, but that confirmation has not been independently assessed.
Sources
Solutions 0
No solutions have been posted yet.