Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions

Details Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions

1997-11-26

arxiv.org/abs/math/9712202v1

Electron. J. Combin. 4 (No. 1) (1997), #R27

Mathematics

Combinatorics

62 pages, AmS-TeX

Scientific paper

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 $(2n)\times(2n)\times(2n)$ 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.

Affiliated with

Also associated with

No associations

Rating

Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-504238