The equivalence between enumerating cyclically symmetric, self-complementary and totally symmetric, self-complementary plane partitions

Cyclically Symmetric Lozenge Tilings of a Hexagon with Four Holes

The work of Mills, Robbins, and Rumsey on cyclically symmetric plane partitions yields a simple product formula for the number of lozenge tilings of a regular hexagon, which are invariant under roation by $120^{\circ}$. In this paper we generalize this result by enumerating the cyclically symmetric lozenge tilings of a hexagon in which four triangles have been removed in the center.

(-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. We use nonintersecting lattice path families to accomplish this for transpose-complementary, cyclically symmetric transpose-complementary and totally symmetric self-complementary plane partitions. For symmetric transpose-complementary and self-complementary plane partitions we get partial results. We also describe Kuperberg's proof for the case of cycl…

有界Littlewood恒等式与交错符号矩阵相关

Bounded Littlewood identity related to alternating sign matrices

本文建立了与交错符号矩阵相关的Littlewood恒等式推广的有界版本，并给出其两边的组合解释，旨在最终构造组合证明以理解交错符号梯形与平面分割对象的关系。