Eliminating Human Insight: An Algorithmic Proof of Stembridge's TSPP Theorem

Details Eliminating Human Insight: An Algorithmic Proof of Stembridge's TSPP Theorem Eliminating Human Insight: An Algorithmic Proof of Stembridge's TSPP Theorem

2009-06-04

arxiv.org/abs/0906.1018v1

Computer Science

Symbolic Computation

12 pages, 4 figures, submitted to Contemporary Mathematics

Scientific paper

We present a new proof of Stembridge's theorem about the enumeration of totally symmetric plane partitions using the methodology suggested in the recent Koutschan-Kauers-Zeilberger semi-rigorous proof of the Andrews-Robbins q-TSPP conjecture. Our proof makes heavy use of computer algebra and is completely automatic. We describe new methods that make the computations feasible in the first place. The tantalizing aspect of this work is that the same methods can be applied to prove the q-TSPP conjecture (that is a q-analogue of Stembridge's theorem and open for more than 25 years); the only hurdle here is still the computational complexity.

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