@article{cameron_coll jr_mayers_russoniello_2023, title={A matrix theory introduction to seaweed algebras and their index}, volume={41}, ISSN={["1878-0792"]}, DOI={10.1016/j.exmath.2023.06.001}, abstractNote={The index of a Lie algebra is an important algebraic invariant, but it is notoriously difficult to compute. However, for the suggestively-named seaweed algebras, the computation of the index can be reduced to a combinatorial formula based on the connected components of a “meander”: a planar graph associated with the algebra. Our index analysis on seaweed algebras requires only basic linear and abstract algebra. Indeed, the main goal of this article is to introduce a broader audience to seaweed algebras with minimal appeal to specialized language and notation from Lie theory. This said, we present several results that do not appear elsewhere and do appeal to more advanced language in the Introduction to provide added context.}, number={4}, journal={EXPOSITIONES MATHEMATICAE}, author={Cameron, Alex and Coll Jr, Vincent E. and Mayers, Nicholas and Russoniello, Nicholas}, year={2023}, month={Dec} }
 @article{mayers_russoniello_2023, title={On toral posets and contact Lie algebras}, volume={190}, ISSN={["1879-1662"]}, DOI={10.1016/j.geomphys.2023.104861}, abstractNote={A (2k+1)-dimensional Lie algebra is called contact if it admits a one-form φ such that φ∧(dφ)k≠0. Here, we extend recent work to describe a combinatorial procedure for generating contact, type-A Lie poset algebras whose associated posets have chains of arbitrary cardinality, and we conjecture that our construction leads to a complete characterization.}, journal={JOURNAL OF GEOMETRY AND PHYSICS}, author={Mayers, Nicholas W. and Russoniello, Nicholas}, year={2023}, month={Aug} }