3 papers
math.PR2025
Monge solutions and uniqueness in multi-marginal optimal transport with hierarchical jumps
Zijian Xu
We introduce Hierarchical Jump multi-marginal transport (HJMOT), a generalization of multi-marginal optimal transport where mass can "jump" over intermediate spaces via augmented i…
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 -dimensional grid of size with no points…
math.CO2024
On -modal subsequences
Zijian Xu
A -modal sequence is a sequence of real numbers that can be partitioned into (possibly empty) monotone sections such that adjacent sections have opposite monotonicities. F…