Enumeration of self-complementary structures
نویسندگان
چکیده
منابع مشابه
(-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...
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متن کاملA Schur function identity related to the (-1)-enumeration of self-complementary plane partitions
We give another proof for the (−1)–enumeration of self-complementary plane partitions with at least one odd side-length by specializing a certain Schur function identity. The proof is analogous to Stanley’s proof for the ordinary enumeration. In addition, we obtain enumerations of 180◦-symmetric rhombus tilings of hexagons with a barrier of arbitrary length along the central line.
متن کاملOn the Doubly Refined Enumeration of Alternating Sign Matrices and Totally Symmetric Self-Complementary Plane Partitions
We prove the equality of doubly refined enumerations of Alternating Sign Matrices and of Totally Symmetric Self-Complementary Plane Partitions using integral formulae originating from certain solutions of the quantum Knizhnik– Zamolodchikov equation. The authors thank N. Kitanine for discussions, and J.-B. Zuber for a careful reading of the manuscript. PZJ was supported by EU Marie Curie Resear...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1978
ISSN: 0095-8956
DOI: 10.1016/0095-8956(78)90034-5