Annals of Combinatorics

, Volume 17, Issue 3, pp 509–523 | Cite as

Advanced Computer Algebra for Determinants

  • Christoph Koutschan
  • Thotsaporn “Aek” Thanatipanonda
Article

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.

Mathematics Subject Classification

33F10 15A15 05B45 

Keywords

determinant computer algebra holonomic ansatz rhombus tiling 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Christoph Koutschan
    • 1
  • Thotsaporn “Aek” Thanatipanonda
    • 1
  1. 1.Research Institute for Symbolic Computation (RISC)Johannes Kepler UniversityLinzAustria

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