Advanced Computer Algebra for Determinants
2013; Birkhäuser; Volume: 17; Issue: 3 Linguagem: Inglês
10.1007/s00026-013-0183-8
ISSN0219-3094
AutoresChristoph Koutschan, Thotsaporn Thanatipanonda,
Tópico(s)Mathematical Dynamics and Fractals
ResumoWe 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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