Symmetries of plane partitions
نویسندگان
چکیده
منابع مشابه
Symmetries of plane partitions
We introduce a new symmetry operation, called complementation, on plane partitions whose three-dimensional diagram is contained in a given box. This operation was suggested by work of Mills, Robbins, and Rumsey. There then arise a total of ten inequivalent problems concerned with the enumeration of plane partitions with a given symmetry. Four of these ten problems had been previously considered...
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In the paper [13], Stanley gives formulas for the number of plane partitions in each of ten symmetry classes. This paper together with the two papers [1] and [14] completes the project of proving all ten formulas. We enumerate cyclically symmetric, self-complementary plane partitions. We first convert plane partitions to tilings of a hexagon in the plane by rhombuses, or equivalently to matchin...
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Throughout our study of the enumeration of plane partitions we make use of bijective proofs to find generating functions. In particular, we consider bounded plane partitions, symmetric plane partitions and weak reverse plane partitions. Using the combinatorial interpretations of Schur functions in relation to semistandard Young tableaux, we rely on the properties of symmetric functions. In our ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1986
ISSN: 0097-3165
DOI: 10.1016/0097-3165(86)90028-2