arXiv subjects

Nguyen Thanh Tung Le

Publications and source records attributed to Nguyen Thanh Tung Le.

2 recordsLinked to original sources

arXiv2025

Generalised Kauffman Clock Theorems

Kauffman's clock theorem provides a distributive lattice structure on the set of states of a four-valent graph in the plane. We prove two distinct generalisations of this theorem, for four-valent graphs embedded in more general compact oriented surfaces. The proofs use results of Propp providing distributive lattice structures on matchings on bipartite plane graphs, and orientations of graphs with fixed circulation.

math.GT↗

arXiv2013

On the existence of orthonormal geodesic bases for Lie algebras

We show that every unimodular Lie algebra, of dimension at most 4, equipped with an inner product, possesses an orthonormal basis comprised of geodesic elements. On the other hand, we give an example of a solvable unimodular Lie algebra of dimension 5 that has no orthonormal geodesic basis, for any inner product.

math.DG↗