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Advanced Computer Algebra for Determinants

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Abstract

We prove three conjectures concerning the evaluation of determinants, which are related to the counting of plane partitions and rhombus tilings. One of them was posed by George Andrews in 1980, the other two were 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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Authors and Affiliations

  1. Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenberger Straße 69, A-4040, Linz, Austria

    Christoph Koutschan & Thotsaporn “Aek” Thanatipanonda

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  1. Christoph Koutschan
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  2. Thotsaporn “Aek” Thanatipanonda
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Correspondence to Christoph Koutschan.

Additional information

CK was supported by the Austrian Science Fund (FWF): P20162-N18, and in part by the grant DMU 03/17 of the Bulgarian National Science Fund. TT was supported by the strategic program “Innovatives OÖ2010plus” by the Upper Austrian Government.

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Koutschan, C., Thanatipanonda, T.“. Advanced Computer Algebra for Determinants. Ann. Comb. 17, 509–523 (2013). https://doi.org/10.1007/s00026-013-0183-8

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  • DOI: https://doi.org/10.1007/s00026-013-0183-8

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