Counterexamples to Stanley's conjecture on dimer coverings

Xuejun Guo, Zhengyu Tao

Let $Q_k(x)$ be Stanley's explicit denominator for the dimer-covering generating function $F_k(x)={\sum }_{n\ge 0}{A}_{k,n}{x}^n$ of $k\times n$ rectangles. Stanley conjectured in 1985 tha…