3 citations · 7 across the 10 of their papers we have counts for
11 papers
Distributions of Ulam Words up to Length 30
Paul Adutwum, Hopper Clark, Ro Emerson +4
We further explore the notion of Ulam words considered by Bade, Cui, Labelle, and Li, giving some lower bounds on how many there are of a given length. Gaps between words and words…
Generating Hyperbolic Isometry Groups by Elementary Matrices
Arseniy, Sheydvasser
We consider three families of groups: the Bianchi groups SL(2,O) where O is the ring of integers of an imaginary, quadratic field; the groups SL*(2,O) where O is a *-order of a def…
Asymptotic Density of Apollonian-Type Packings
Matthew Litman, Arseniy Sheydvasser
We consider two seemingly unconnected problems: first, under what circumstances are arithmetic groups like SL(2,O) generated by elementary matrices; second, when do certain classes…
Algebraic Groups Constructed From Rings with Involution
Arseniy Sheydvasser
We define a class of groups constructed from rings equipped with an involution. We show that under suitable conditions, these groups are either algebraic or arithmetic, including a…
The Twisted Euclidean Algorithm: Applications to Number Theory and Geometry
Arseniy, Sheydvasser
We introduce a generalization of the Euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes of orders over definite, rational q…
The Ulam Sequence of the Integer Polynomial Ring
Arseniy Sheydvasser
An Ulam sequence U(1,n) is defined as the sequence starting with integers 1,n such that n > 1, and such that every subsequent term is the smallest integer that can be written as th…