#group theory
11 papers · 1 filter
Group-theoretic treatment of strong light-matter coupling with an arbitrary number of excitations
Antti Peltola, Olli Siltanen, Kimmo Luoma +1
The paper develops a group‑theoretic framework for the Tavis‑Cummings model with any number of excitations, deriving its eigensystem and allowed radiative transitions, and showing…
Constructing linear codes from digraphs and groups
Coen del Valle, Cheryl E. Praeger
The paper extends the Cayley code construction by introducing graph and digraph codes, analyzes their algebraic and combinatorial properties, and shows they can yield good LDPC cod…
Schreier-Coset Graph Rewiring
Aryan Mishra, Randy Martinez, Lizhen Lin
The paper proposes Schreier-Coset Graph Rewiring, a group‑theoretic method that augments a graph with a Schreier‑Coset graph to reduce over‑squashing in graph neural networks while…
Learning the Word Problem: Geodesic Lengths and Cryptographic Applications
Elisabeth Fink
The paper presents WPNet, a graph neural network that learns to solve the Word Problem and predict geodesic lengths in certain infinite groups, and shows how this can be used to at…
On the Darboux Integrability of the Constant Mean Curvature One Equation for Surfaces in Hyperbolic 3 space
Mark E. Fels, Thomas A. Ivey
The paper proves that the elliptic PDE system governing constant mean curvature one immersions in hyperbolic 3‑space is Darboux integrable and equivalent to the elliptic Liouville…
Groups with Finitely Many Shortlex Cones
LucÃa Asencio-MartÃn, Paloma López-Larios
The paper proves that any finitely generated group with the falsification‑by‑fellow‑traveller property also satisfies its shortlex version, yielding finitely many shortlex cone typ…