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,…
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 Stembr…
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…
Hopf algebras of parking functions and decorated planar trees
Nantel Bergeron, Rafael S. González D'León, Shu Xiao Li +2
We construct three new combinatorial Hopf algebras based on the Loday-Ronco operations on planar binary trees. The first and second algebras are defined on planar trees and labeled…