TY - UNPB
T1 - Advanced Computer Algebra for Determinants
AU - Koutschan, Christoph
AU - Thanatipanonda, Thotsaporn
PY - 2011
Y1 - 2011
N2 - We prove three conjectures concerning the evaluation of determinants, which are related to the counting of plane partitions and rhombus tilings. One of them has been posed by George Andrews in 1980, the other two are 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.
AB - We prove three conjectures concerning the evaluation of determinants, which are related to the counting of plane partitions and rhombus tilings. One of them has been posed by George Andrews in 1980, the other two are 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.
UR - http://risc.jku.at/people/ckoutsch/det/
M3 - Preprint
T3 - arXiv.org
BT - Advanced Computer Algebra for Determinants
ER -