5 citations · 6 across the 10 of their papers we have counts for
10 papers
A rock-paper-scissors Mandelbrot set
Charlotte Aten
The titular object of this paper is an analogue of the Mandelbrot set over the 3-dimensional real algebra whose multiplication is the bilinear extension of the rock-paper-scissors…
Higher-dimensional book-spaces
Charlotte Aten
In 2017, Walter Taylor showed that there exist -dimensional simplicial complexes which admit the structure of topological modular lattice but not topological distributive lattic…
Invariants of structures
Charlotte Aten
We give a categorification of the notion of a mathematical structure originally given by Bourbaki in their set theory textbook. We show that any isomorphism-invariant property of a…
A partition formula from idempotents
Charlotte Aten
A formula which only involves a partition number and elementary functions is derived by applying Burnside's Lemma to the set of idempotent maps from a set to itself. One side invol…
Discrete neural nets and polymorphic learning
Charlotte Aten
Theorems from universal algebra such as that of Murskiĭ from the 1970s have a striking similarity to universal approximation results for neural nets along the lines of Cybenko's fr…
Phase behavior of a cell model with Curie-Weiss interaction
M. P. Kozlovskii, O. A. Dobush
The object of this study is a cell model with Curie-Weiss interaction potential. We have already proved the possibility of a mathematically rigorous transition from a continuous sy…
Orientable triangulable manifolds are essentially quasigroups
Charlotte Aten, Semin Yoo
We introduce an -dimensional analogue of the construction of tessellated surfaces from finite groups first described by Herman and Pakianathan. Our construction is functorial an…
Multiplayer Rock-Paper-Scissors
Charlotte Aten
We study a class of algebras we regard as generalized Rock-Paper-Scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generate…
Nonnormal Quotients
Charlotte Aten
We present a natural extension of the process of taking a group quotient to arbitrary subgroups. We first review basic concepts from group theory. This will allow us to see the rel…
Tiling sets and spectral sets over finite fields
C. Aten, B. Ayachi, E. Bau +14
We study tiling and spectral sets in vector spaces over prime fields. The classical Fuglede conjecture in locally compact abelian groups says that a set is spectral if and only if…