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.
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 509–523 |
| Seitenumfang | 15 |
| Fachzeitschrift | Annals of Combinatorics |
| Volume | 17 |
| Ausgabenummer | 3 |
| DOIs | |
| Publikationsstatus | Veröffentlicht - Sep. 2013 |
Wissenschaftszweige
- 101001 Algebra
- 101002 Analysis
- 101 Mathematik
- 102 Informatik
- 102011 Formale Sprachen
- 101009 Geometrie
- 101013 Mathematische Logik
- 101020 Technische Mathematik
- 101025 Zahlentheorie
- 101012 Kombinatorik
- 101005 Computeralgebra
- 101006 Differentialgeometrie
- 101003 Angewandte Geometrie
- 102025 Verteilte Systeme
JKU-Schwerpunkte
- Computation in Informatics and Mathematics
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