5 papers · 1 filter
The index and spectrum of Lie poset algebras of type B, C, and D
Vincent E. Coll, Nicholas W. Mayers
In this paper, we define posets of types B, C, and D. These posets encode the matrix forms of certain Lie algebras which lie between the algebras of upper-triangular and diagonal m…
The index of Lie poset algebras
Vincent E. Coll, Nick W. Mayers
We provide general closed-form formulas for the index of type-A Lie poset algebras corresponding to posets of restricted height. Furthermore, we provide a combinatorial recipe for…
Statistics on integer partitions arising from seaweed algebras
Vincent Coll, Andrew Mayers, Nick Mayers
Using the index theory of seaweed algebras, we explore various new integer partition statistics. We find relations to some well-known varieties of integer partitions as well as a s…
On compositions associated to seasweed subalgebras of sl(n)
Vincent E. Coll, Aria Dougherty, Matthew Hyatt +2
A standard seaweed subalgebra of may be parametrized by a pair of compositions of the positive integer . For all and certain , we provide cl…
How to Build a Graph in n Days: Some Variants on Graph Assembly
Aria Dougherty, Nick Mayers, Robert Short
In a recent article by M. Bona and A. Vince, the authors introduced the concept of an assembly tree for a graph. Assembly trees act as record keeping devices for the construction o…