Plane Partitions I: a Generalization of Macmahon’s Formula
نویسنده
چکیده
The number of plane partitions contained in a given box was shown by MacMahon [8] to be given by a simple product formula. By a simple bijection, this formula also enumerates lozenge tilings of hexagons of side-lengths a, b, c, a, b, c (in cyclic order) and angles of 120 degrees. We present a generalization in the case b = c by giving simple product formulas enumerating lozenge tilings of regions obtained from a hexagon of side-lengths a, b + k, b, a + k, b, b + k (where k is an arbitrary non-negative integer) and angles of 120 degrees by removing certain triangular regions along its symmetry axis.
منابع مشابه
A Generalization of Macmahon’s Formula
We generalize the generating formula for plane partitions known as MacMahon’s formula as well as its analog for strict plane partitions. We give a 2-parameter generalization of these formulas related to Macdonald’s symmetric functions. The formula is especially simple in the Hall-Littlewood case. We also give a bijective proof of the analog of MacMahon’s formula for strict plane partitions.
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