Determinants in Enumerative Combinatorics

• Presentation
• Mathematica notebook
• Mathematica notebook in PDF
• Exercises

Literature

• Christian Krattenthaler, Advanced determinant calculus, Séminaire Lotharingien Combin. 42 ("The Andrews Festschrift") (1999), Article B42q, 67 pp.
• Christian Krattenthaler, Advanced determinant calculus: a complement, Linear Algebra Appl. 411 (2005), 68-166.
• Sylvie Corteel and Jang Soo Kim, Lecture hall tableaux, Adv. Math. 371 (2020), 107266, 35 pp.
• Tewodros Amdeberhan, Christoph Koutschan, Doron Zeilberger, Yay for Determinants!, preprint, arχiv:2307.01912
• Proof of Jacobi's condensation formula
• Christian Krattenthaler, An alternative evaluation of the Andrews-Burge determinant, in: Mathematical Essays in Honor of Gian-Carlo Rota, B. E. Sagan, R. P. Stanley (eds.), Progress in Math., vol. 161, Birkhäuser, Boston, 1998, pp. 263-270.
• George Andrews and Dennis Stanton, Determinants in plane partition enumeration, Europ. J. Combin. 19 (1998), 273-282.
• Doron Zeilberger, The holonomic ansatz. II. Automatic discovery(!) and proof(!!) of holonomic determinant evaluations, Ann. Comb. 11 (2007), 241-247.
• Hao Du, Christoph Koutschan, Thotsaporn Thanatipanonda and Elaine Wong, Binomial determinants for tiling problems yield to the holonomic ansatz, European J. Combin. 99 (2022), Paper No. 103437, 40 pp.
• Xavier Viennot, Une théorie combinatoire des polynômes orthogonaux, Lecture Notes LACIM, Université de Québéc à Montréal, 1984.
• John R. Stembridge, Nonintersecting paths, pfaffians and plane partitions, Adv. in Math. 83 (1990), 96-131.
• Glenn Tesler, Matchings in graphs on non-orientable surfaces, J. Combin. Theory Ser. B78 (2000), 198-231.

Links to Software

• ErgoSum (Zeilberger algorithm, Guessing recurrences, HolonomicFunctions, ...)
• Rate