Enumeration of Cylindric Plane Partitions

Résumé. Cylindric plane partitions may be thought of as a natural generalization of reverse plane partitions. A generating series for the enumeration of cylindric plane partitions was recently given by Borodin. As in the reverse plane partition case, the right hand side of this identity admits a simple factorization form in terms of the “hook lengths” of the individual boxes in the underlying shape. The first result of this paper is a new bijective proof of Borodin’s identity which makes use of Fomin’s growth diagram framework for generalized RSK correspondences. The second result of this paper is a (q, t)-analog of Borodin’s identity which extends previous work by Okada in the reverse plane partition case. The third result of this paper is an explicit combinatorial interpreation of the Macdonald weight occuring in the (q, t)-analog in terms of the non-intersecting lattice path model for cylindric plane partitions.