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math.CO2025
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,…
math.CO2025
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…
math.CO2021
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…