Counting solid Young tableaux of shape [[n,n],[n,1]]
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Let g(n) count solid standard Young tableaux of the two-layer shape [[n,n],[n,1]]. Does it satisfy the conjectured second-order polynomial recurrence of degree 12 for every n≥1?
Why it matters and what counts as progress
Why it matters: An all-n recurrence explains an enumerative sequence beyond agreement with a finite table.
What counts as progress: A proved recurrence with initial conditions, an explicit formula implying it, or a term rigorously violating the conjectured recurrence.
How the problem developed
- 28 Feb 2012 · Challenge and computational evidence [1]
Shalosh B. Ekhad and Doron Zeilberger, with data from Manuel Kauers and Fredrik Johansson Posed a recurrence challenge for the shape [[n,n],[n,1]]; added data showed that 6,000 terms were insufficient to identify a recurrence in the searched order and degree ranges.
- 11 Aug 2026 · Reported theorem [2]
Jaideep Sai Padhi Reported a proof of the conjectured second-order recurrence for the solid standard Young tableau counts of this shape.
AI contribution
Solutions to Five Challenge Problems in Enumerative and Algorithmic Combinatorics, with an Account of the Human-Machine Methodology Employed
For the two-layer solid standard Young-tableau shape [[n,n],[n,1]], Padhi gives an explicit two-term hypergeometric formula for the count g(n) and proves the conjectured second-order degree-12 recurrence for every n≥1.
Sources
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