From the 1 of 5 linked papers with an AI index.
5 papers
An affirmative answer to Owings's sumset question
Wen Huang, Zhengxing Lian, Song Shao +3
We give an affirmative answer to Owings's sumset question: for any -coloring of natural numbers, there is an infinite such that is monochromatic. Mo…
MathCoPilot: An Interactive System for Human-AI Symbiotic Paradigm of Mathematical Research
Junjie Zhang, Jiayu Liu, Wenbin Liu +11
MathCoPilot is an interactive, human‑in‑the‑loop system that lets mathematicians steer AI agents to formalize and verify mathematical proofs in Lean, combining a live proof bluepri…
Typical periodic optimization for dynamical systems: symbolic dynamics
Wen Huang, Oliver Jenkinson, Leiye Xu +1
We develop a new theory of maximizing sets in dynamical systems, for the study of ergodic optimization in systems with weak hyperbolicity but where the Mañé cohomology lemma does…
Almost Countable Spectrum and Logarithmic Sarnak Conjecture
Wen Huang, Maoru Tan, Leiye Xu
In this paper, we introduce topological dynamical systems with almost countable spectrum. We prove that the Logarithmic Sarnak Conjecture holds for zero-entropy topological dynamic…
Directional Pinsker algebra and its applications
Chunlin Liu, Leiye Xu
In this paper, we introduce the directional Pinsker algebra, and construct a skew product to study it. As applications, we show that 1. if a -system with positive dir…