Xue-Jun Guo

collaborators

2 papers

math.CO2026

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 $F_{k} (x) = \sum_{n \geq 0} A_{k, n} x^{n}$ of $k \times n$ rectangles. Stanley conjectured in 1985 tha…

math.NT2023

CM points, class numbers, and the Mahler measures of $x^{3} + y^{3} + 1 - k x y$

Zhengyu Tao, Xuejun Guo

We study the Mahler measures of the polynomial family $Q_{k} (x, y) = x^{3} + y^{3} + 1 - k x y$ using the method previously developed by the authors. An algorithm is implemented to search for CM…

Counterexamples to Stanley's conjecture on dimer coverings

CM points, class numbers, and the Mahler measures of x3+y3+1−kxy

CM points, class numbers, and the Mahler measures of $x^{3} + y^{3} + 1 - k x y$