4 papers
math.CO2026
Extremal Spanning Trees in Product Grid Graphs
Jiechen Zhang
We study how fixed-volume spanning-tree extremality changes when product-grid boundary factors are free, periodic, or mixed. In two dimensions, extremality depends sharply on the b…
math.CO2026
The Balancing Theorem for Spanning Trees of Rectangular Grid Graphs
Jiechen Zhang
We compare spanning-tree counts of rectangular grid graphs at fixed area. The main result is a balancing theorem: if and , then the more balanced rectangl…
math.PR2026
Threshold Rules for the Classical Prophet Inequality
Jiechen Zhang
This note records a common threshold/surplus decomposition for single-threshold stopping rules in the classical prophet inequality. The same decomposition is used to certify severa…
math.PR2026
Explicit Universal Bounds for Cumulants via Moments
Jiechen Zhang
We establish explicit, universal, and distribution-free bounds for the -th cumulant, , of a scalar random variable, controlled solely by an -th order absolute moment…