2 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…