2026/06/11 by Jean-Luc Baril, José Luis Ramírez, Samuel Ramírez +1 · 1 voice
Computer Science · #cs.DM
paper · pdf · doi:10.4204/eptcs.445.3
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.