Enumeration of Cylindric Plane Partitions - part I

Details Enumeration of Cylindric Plane Partitions - part I Enumeration of Cylindric Plane Partitions - part I

2012-04-20

arxiv.org/abs/1204.4583v1

Mathematics

Combinatorics

Scientific paper

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. The first 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. Our proof uses commutation relations for $(q,t)$-vertex operators acting on Macdonald polynomials as given by Garsia, Haiman and Tesla. The second result of this paper is an explicit combinatorial interpreation of the $(q,t)$-Macdonald weight in terms of a non-intersecting lattice path model on the cylinder.

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