2 citations · 5 across the 9 of their papers we have counts for
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Visible lattice points in Pólya's walk
Meijie Lu, Xianchang Meng
In this paper, for any integer , we study the distribution of the visible lattice points in certain generalized Pólya's walk on : perturbed Pólya's walk and…
Visible lattice points in higher dimensional random walks and biases among them
Kui Liu, Meijie Lu, Xianchang Meng
For any integers , and any finite set , where ${ \boldsymbolα_t}=(α_{t,1},\cdots,α_{t,k})~(1\leq t\leq…
Random walks on generalized visible lattice points
Kui Liu, Xianchang Meng
We consider the proportion of generalized visible lattice points in the plane visited by random walkers. Our work concerns the visible lattice points in random walks in three aspec…
Distinct distances on hyperbolic surfaces
Xianchang Meng
For any cofinite Fuchsian group , we show that any set of points on the hyperbolic surface determines $\geq C_Γ \fr…
Erdős distinct distances in hyperbolic surfaces
Zhipeng Lu, Xianchang Meng
In this paper, we introduce the notion of "geodesic cover" for Fuchsian groups, which summons copies of fundamental polygons in the hyperbolic plane to cover pairs of representativ…
Visible lattice points along curves
Kui Liu, Xianchang Meng
This paper concerns the number of lattice points in the plane which are visible along certain curves to all elements in some set S of lattice points simultaneously. By proposing th…