  The forcing number of a perfect matching $M$ in a graph $G$ is the smallest
number of edges inside $M$ that can not be contained in other perfect
matchings. The anti-forcing number of $M$ is the smallest number of edges
outside $M$ whose removal results in a subgraph with a single perfect matching,
that is $M$. Recently, in order to investigate the distributions of forcing
numbers and anti-forcing numbers, the forcing polynomial and anti-forcing
polynomial were proposed, respectively. In this work, the forcing and
anti-forcing polynomials of a polyomino graph are obtained. As consequences,
the forcing and anti-forcing spectra of this polyomino graph are determined,
and the asymptotic behaviors on the degree of freedom and the sum of all
anti-forcing numbers are revealed, respectively.
