Publication: A curious family of binomial determinants that count rhombus tilings of a holey hexagon
Issued Date
2019-08-01
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ISSN
10960899
00973165
00973165
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2-s2.0-85063887376
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Mahidol University
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SCOPUS
Bibliographic Citation
Journal of Combinatorial Theory. Series A. Vol.166, (2019), 352-381
Suggested Citation
Christoph Koutschan, Thotsaporn Thanatipanonda A curious family of binomial determinants that count rhombus tilings of a holey hexagon. Journal of Combinatorial Theory. Series A. Vol.166, (2019), 352-381. doi:10.1016/j.jcta.2019.03.001 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/50620
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Title
A curious family of binomial determinants that count rhombus tilings of a holey hexagon
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Abstract
© 2019 Elsevier Inc. We evaluate a curious determinant, first mentioned by George Andrews in 1980 in the context of descending plane partitions. Our strategy is to combine the famous Desnanot-Jacobi-Dodgson identity with automated proof techniques. More precisely, we follow the holonomic ansatz that was proposed by Doron Zeilberger in 2007. We derive a compact and nice formula for Andrews's determinant, and use it to solve a challenge problem that we posed in a previous paper. By noting that Andrews's determinant is a special case of a two-parameter family of determinants, we find closed forms for several one-parameter subfamilies. The interest in these determinants arises because they count cyclically symmetric rhombus tilings of a hexagon with several triangular holes inside.