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.
| Original language | English |
|---|---|
| Pages (from-to) | 509–523 |
| Number of pages | 16 |
| Journal | Annals of Combinatorics |
| Volume | 17 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2013 |
Fields of science
- 101001 Algebra
- 101002 Analysis
- 101 Mathematics
- 102 Computer Sciences
- 102011 Formal languages
- 101009 Geometry
- 101013 Mathematical logic
- 101020 Technical mathematics
- 101025 Number theory
- 101012 Combinatorics
- 101005 Computer algebra
- 101006 Differential geometry
- 101003 Applied geometry
- 102025 Distributed systems
JKU Focus areas
- Computation in Informatics and Mathematics