反演关系、互反性与多联骨牌
Inversion relations, reciprocity and polyominoes
AI总结：
本文推导多联骨牌生成函数的自互反性质，并建立组合互反结果与统计力学反演关系的联系，从而完全确定若干凸多边形的各向异性周长生成函数。
摘要：
我们推导了若干多联骨牌生成函数的自互反性质，包括几类列凸多边形、三选多边形以及带阶梯孔阶梯多边形的生成函数。在此过程中，我们建立了组合学家已知的互反结果与物理学家用于求解统计力学模型的反演关系之间的联系。对于几类凸多边形，反演（互反）关系加上某些对称性和解析性质，完全确定了各向异性周长生成函数。
英文摘要：
We derive self-reciprocity properties for a number of polyomino generating functions, including several families of column-convex polygons, three-choice polygons and staircase polygons with a staircase hole. In so doing, we establish a connection between the reciprocity results known to combinatorialists and the inversion relations used by physicists to solve models in statistical mechanics. For several classes of convex polygons, the inversion (reciprocity) relation, augmented by certain symmetry and analyticity properties, completely determines the anisotropic perimeter generating function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
