8 papers
Some results on Archdeacon's conjecture for rotation systems
Arahat Chikkatur, Ji Zeng
A rotation system on elements assigns to each element a cyclic order of the other elements. A four-element subset is non-planar if its induced rotation system cannot be r…
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+…
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…
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…
Ordered Yao graphs: maximum degree, edge density, and clique numbers
Péter Ágoston, 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…
Unbalanced Zarankiewicz problem for bipartite subdivisions with applications to incidence geometry
Lili Ködmön, Anqi Li, Ji Zeng
For a bipartite graph , its linear threshold is the smallest real number such that every bipartite graph with unbalanced parts and…
Saturation results around the Erdős--Szekeres problem
Gábor Damásdi, Zichao Dong, Manfred Scheucher +1
In this paper, we consider saturation problems related to the celebrated Erdős--Szekeres convex polygon problem. For each , we construct a planar point set of size $(7/8)…