7 papers
On balanced circuits in uniform rank-three oriented matroids
Ji Zeng
A set of four points on the sphere is a balanced quadruple if there are four real numbers , two positive and two negative, such that $s_1p_1+…
Ordered Yao graphs: maximum degree, edge density, and clique numbers
Péter Ãgoston, Adrian Dumitrescu, Arsenii Sagdeev +2
For a positive integer and an ordered set of points in the plane, define its \textit{k-sector ordered Yao graphs} as follows. Divide the plane around each point into eq…
To cover a permutohedron
Bochao Kong, Ji Zeng
The permutohedron of order is a polytope embedded in whose vertex coordinates are permutations of the first natural numbers. It is obvious that l…
Saturation results around the ErdÅs--Szekeres problem
Gábor Damásdi, Zichao Dong, Manfred Scheucher +1
In this paper, we consider saturation problems related to the celebrated ErdÅs--Szekeres convex polygon problem. For each , we construct a planar point set of size $(7/8)…
Most Fatou and Julia components are small for polynomials
Jinsong Zeng
We prove that Julia components of polynomials are generally small in diameter. For polynomials without irrationally neutral cycles, Fatou components are also typically small, even…
Evasive sets, twisted varieties, and container-clique trees
Jeck Lim, Jiaxi Nie, Ji Zeng
In the affine space over the finite field of order , a point set is said to be -evasive if the intersection between and any variety, of dimensi…