3 papers
math.CO2026
A Hopf algebra on nonplanar binary forests
Elizabeth Xiao
We equip the graded polynomial algebra generated by nonplanar rooted binary trees with a Hopf algebra structure by defining a coproduct which disallows cutting both children of any…
cs.CL2025
A Lie-algebraic perspective on Tree-Adjoining Grammars
Isabella Senturia, Elizabeth Xiao, Matilde Marcolli
We provide a novel mathematical implementation of tree-adjoining grammars using two combinatorial definitions of graphs. With this lens, we demonstrate that the adjoining operation…
math.CO2022
On the anisotropy theorem of Papadakis and Petrotou
Kalle Karu, Elizabeth Xiao
We study the anisotropy theorem for Stanley-Reisner rings of simplicial homology spheres in characteristic 2 by Papadakis and Petrotou. This theorem implies the Hard Lefschetz theo…