Advanced Computer Algebra for Determinants

Details Advanced Computer Algebra for Determinants Advanced Computer Algebra for Determinants

2011-12-03

arxiv.org/abs/1112.0647v2

Computer Science

Symbolic Computation

16 pages

Scientific paper

We prove three conjectures concerning the evaluation of determinants, which are related to the counting of plane partitions and rhombus tilings. One of them has been posed by George Andrews in 1980, the other two are by Guoce Xin and Christian Krattenthaler. Our proofs employ computer algebra methods, namely the holonomic ansatz proposed by Doron Zeilberger and variations thereof. These variations make Zeilberger's original approach even more powerful and allow for addressing a wider variety of determinants. Finally we present, as a challenge problem, a conjecture about a closed form evaluation of Andrews's determinant.

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