Enumeration of plane partitions
نویسندگان
چکیده
منابع مشابه
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 s...
متن کامل(-1)-Enumeration of Self-Complementary Plane Partitions
Abstract. We prove a product formula for the remaining cases of the weighted enumeration of self–complementary plane partitions contained in a given box where adding one half of an orbit of cubes and removing the other half of the orbit changes the sign of the weight. We use nonintersecting lattice path families to express this enumeration as a Pfaffian which can be expressed in terms of the kn...
متن کامل(−1)–enumeration of Plane Partitions with Complementation Symmetry
We compute the weighted enumeration of plane partitions contained in a given box with complementation symmetry where adding one half of an orbit of cubes and removing the other half of the orbit changes the weight by −1 as proposed by Kuperberg in [7, pp.25/26]. We use nonintersecting lattice path families to accomplish this for transpose–complementary, cyclically symmetric transpose–complement...
متن کاملEnumeration of M-partitions
An M-partition of a positive integer m is a partition of m with as few parts as possible such that every positive integer less than m can be written as a sum of parts taken from the partition. This type of partition is a variation of MacMahon’s perfect partition, and was recently introduced and studied by O’Shea, who showed that for half the numbers m, the number of M-partitions of m is equal t...
متن کاملEnumeration of Concave Integer Partitions
An integer partition λ ` n corresponds, via its Ferrers diagram, to an artinian monomial ideal I ⊂ C[x, y] with dimC C[x, y]/I = n. If λ corresponds to an integrally closed ideal we call it concave . We study generating functions for the number of concave partitions, unrestricted or with at most r parts. 1. concave partitions By an integer partition λ = (λ1, λ2, λ3, . . . ) we mean a weakly dec...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1972
ISSN: 0097-3165
DOI: 10.1016/0097-3165(72)90007-6