Generating functions for shifted plane partitions
نویسنده
چکیده
With the help of a tableaux method, determinant formulas for trace generating functions for various classes of shifted plane partitions are derived. Proceeding from these determinants, generalizations of Gansner's (J. hook formulas for shifted plane partitions and alternative proofs of recent results of Proctor about alternating trace generating functions are given.
منابع مشابه
Combinatorial Proofs of Hook Generating Functions for Skew Plane Partitions
Sagan, B.E., Combinatorial proofs of hook generating functions for skew plane partitions, Theoretical Computer Science 117 (1993) 273-287. We provide combinatorial proofs of two hook generating functions for skew plane partitions. One proof involves the Hillman-Grass1 (1976) algorithm and the other uses a modification of Schiitzenberger’s (1963, 1977) “jeu de taquin” due to Kadell (to appear). ...
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We generalize multivariate hook product formulae for P -partitions. We use Macdonald symmetric functions to prove a (q, t)-deformation of Gansner’s hook product formula for the generating functions of reverse (shifted) plane partitions. (The unshifted case has also been proved by Adachi.) For a d-complete poset, we present a conjectural (q, t)-deformation of Peterson–Proctor’s hook product form...
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We generalize multivariate hook product formulae for P -partitions. We use Macdonald symmetric functions to prove a (q, t)-deformation of Gansner’s hook product formula for the generating functions of reverse (shifted) plane partitions. For a d-complete poset, we present a conjectural (q, t)-deformation of Peterson–Proctor’s hook product formula.
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