Asymptotic counts of three-row tableaux with restricted runs
Follow the latest progress by email.
For standard Young tableaux with three rows, what are the asymptotic counts when every run has length at least two, or when every run length is odd? The conjectured exponential bases are 8 and 7+5√2, respectively, with an n⁻⁴ factor.
Why it matters and what counts as progress
Why it matters: Exact asymptotics explain growth beyond finite enumerations and numerical guesses.
What counts as progress: A proof of each growth law with a positive finite leading constant, or a correction to its exponent, base or constant.
How the problem developed
- 2020 · Conjecture [1]
Manuel Kauers and Doron Zeilberger Proposed asymptotics for three-row standard Young tableaux with every run of length at least two, and with all run lengths odd.
- 11 Aug 2026 · Reported claim [2]
Jaideep Sai Padhi, in collaboration with Claude Proved the two conjectured forms: G(n)∼C₁8ⁿ/n⁴ and H(n)∼C₂(7+5√2)ⁿ/n⁴, with explicit positive constants.
AI contribution
Solutions to Five Challenge Problems in Enumerative and Algorithmic Combinatorics, with an Account of the Human-Machine Methodology Employed
For three-row tableaux with runs of length at least two, G(n)~C₁8ⁿ/n⁴; for odd runs, H(n)~C₂(7+5√2)ⁿ/n⁴. The constants are positive finite boundary sums, with numerical estimates about 0.52128605909 and 0.6389278129.
Sources
Website timeline
Publication dates and editorial changes.