13 citations · 16 across the 7 of their papers we have counts for
7 papers
The realization of input-output maps using bialgebras
Robert L. Grossman, Richard G. Larson
We use the theory of bialgebras to provide the algebraic background for state space realization theorems for input-output maps of control systems. This allows us to consider from a…
State Space Realization Theorems For Data Mining
Robert L Grossman, Richard G Larson
In this paper, we consider formal series associated with events, profiles derived from events, and statistical models that make predictions about events. We prove theorems about re…
Hopf-algebraic structures of families of trees
R. L. Grossman, R. G. Larson
Description of cocommutative Hopf algebras associated with families of trees. Applications include Cayley's theorem on the number of rooted trees with n nodes, and Catalan's theore…
An Overview of Hopf Algebras of Trees and Their Actions on Functions
Robert L. Grossman, Richard G. Larson
We provide an expository account of some of the Hopf algebras that can be defined using trees, labeled trees, ordered trees and heap ordered trees. We also describe some actions of…
Hopf Algebras of Heap Ordered Trees and Permutations
R. L. Grossman, R. G. Larson
It is known that there is a Hopf algebra structure on the vector space with basis all heap-ordered trees. We give a new bialgebra structure on the space with basis all permutations…
Some combinatorial aspects of movies and movie-moves in the theory of smoothly knotted surfaces in R4
Glenn Lancaster, Richard Larson, Jacob Towber
For proper subsets U of {1,2,...,31} we define and construct U-regular isotopy invariants of the Carter-Rieger-Saito movies (representing knotted surfaces) and use these to show th…