Zijian Xu

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math.CO2025

Large grid subsets without many cospherical points

Zichao Dong, Zijian Xu

Motivated by intuitions from projective algebraic geometry, we provide a novel construction of subsets of the $d$ -dimensional grid $[n]^{d}$ of size $n - o (n)$ with no $d + 2$ points…

math.CO2024

On $k$ -modal subsequences

Zijian Xu

A $k$ -modal sequence is a sequence of real numbers that can be partitioned into $k + 1$ (possibly empty) monotone sections such that adjacent sections have opposite monotonicities. F…

Large grid subsets without many cospherical points

On k-modal subsequences

On $k$ -modal subsequences