4 papers
How to Use Deep Learning to Identify Sufficient Conditions: A Case Study on Stanley's -Positivity
Farid Aliniaeifard, Shu Xiao Li
In a study, published in Nature, researchers from DeepMind and mathematicians demonstrated a general framework using machine learning to make conjectures in pure mathematics. Here,…
Extending the descent-to-peak map and its applications
Farid Aliniaeifard, Shu Xiao Li
The descent-to-peak map serves as a bridge between algebra and combinatorics. We use it as a tool for proving the equidistribution of peak and valley sets of standard Young tableau…
The peak algebra in noncommuting variables
Farid Aliniaeifard, Shu Xiao Li
The well-known descent-to-peak map for the Hopf algebra of quasisymmetric functions, , and the peak algebra were originally defined by Stem…
Commutators with multiple unitary symmetry
Shu Li, Jie Wang, Binfeng Wang +1
Commutators are essential in quantum information theory, influencing quantum state symmetries and information storage robustness. This paper systematically investigates the charact…