1997/11/26 by Christian Krattenthaler
Mathematics · #math.CO #msc:05A15 #msc:05A17 #msc:15A15 #msc:33C20
published as Electron. J. Combin. 4 (No. 1) (1997), #R27 · 62 pages, AmS-TeX
arxiv created 1997/11/26 · arxiv updated 2009/11/30
We prove a constant term conjecture of Robbins and Zeilberger (J. Combin. Theory Ser. A 66 (1994), 17-27), by translating the problem into a determinant evaluation problem and evaluating the determinant. This determinant generalizes the determinant that gives the number of all totally symmetric self-complementary plane partitions contained in a (2n)×(2n)×(2n) box and that was used by Andrews (J. Combin. Theory Ser. A 66 (1994), 28-39) and Andrews and Burge (Pacific J. Math. 158 (1993), 1-14) to compute this number explicitly. The evaluation of the generalized determinant is independent of Andrews and Burge's computations, and therefore in particular constitutes a new solution to this famous enumeration problem. We also evaluate a related determinant, thus generalizing another determinant identity of Andrews and Burge (loc. cit.). By translating some of our determinant identities into constant term identities, we obtain several new constant term identities.