We study Fibonacci (staircase) polyominoes, a class of column-convex polyominoes whose lower boundary is a staircase with unit vertical steps. We derive multivariate generating functions that refine Turban's Fibonacci-number enumeration by tracking additional perimeter and area parameters. The proofs use a catalytic functional equation and, in a perimeter specialization, the kernel method, leading to explicit closed forms and Catalan-number coefficient formulas.

翻译：本文研究斐波那契（阶梯）多联骨牌，这是一类列凸多联骨牌，其下边界为具有单位垂直步长的阶梯。我们推导了多变量生成函数，通过追踪额外的周长和面积参数，细化了Turban基于斐波那契数的枚举。证明过程使用了催化泛函方程，并在周长特化情形下运用核方法，得到了显式的封闭形式及卡塔兰数系数公式。