21 citations · 37 across the 13 of their papers we have counts for
14 papers
Kronecker Products, Polarity Quotients and Large Graph Constructions
Kelly Isham, Kartik Lakhotia, Laura Monroe +1
In this paper, we establish a structural compatibility between the Kronecker product of bipartite graphs that admit polarity and their polarity quotients, and provide a sharp upper…
Configurations of 10 points and their incidence varieties
Kelly Isham, Nathan Kaplan, Sam Kimport +3
Incidence varieties are spaces of -tuples of points in the projective plane that satisfy a given set of collinearity conditions. We classify the components of incidence varietie…
Most subrings of have large corank
Gautam Chinta, Kelly Isham, Nathan Kaplan
If is a sublattice of index , then is a finite abelian group of order and rank at most . Several authors have studied statistic…
Edge-Disjoint Spanning Trees on Star-Product Networks
Kelly Isham, Laura Monroe, Kartik Lakhotia +3
A star-product operation may be used to create large graphs from smaller factor graphs. Network topologies based on star-products demonstrate several advantages including low-diame…
Generalized Eckardt points on del Pezzo surfaces of degree 1
Julie Desjardins, Yu Fu, Kelly Isham +1
We study intersections of exceptional curves on del Pezzo surfaces of degree 1, motivated by questions in arithmetic geometry. Outside characteristics 2 and 3, at most 10 exception…
PolarStar: Expanding the Scalability Horizon of Diameter-3 Networks
Kartik Lakhotia, Laura Monroe, Kelly Isham +4
We present PolarStar, a novel family of diameter-3 network topologies derived from the star product of low-diameter factor graphs. PolarStar gives the largest known diameter-3 netw…
PolarFly: A Cost-Effective and Flexible Low-Diameter Topology
Kartik Lakhotia, Maciej Besta, Laura Monroe +4
In this paper we present PolarFly, a diameter-2 network topology based on the Erdos-Renyi family of polarity graphs from finite geometry. This is a highly scalable low-diameter top…
An algorithm to count the number of caps in
Kelly Isham
An -cap in -dimensional projective space is a set of points so that no three lie on a line. In this note, we provide an algorithm to count the number of -caps in $\mat…
Is the number of subrings of index in polynomial in ?
Kelly Isham
It is well-known that for each fixed and , the number of subgroups of index in is a polynomial in . Is this true for \emph{subrings} in $\mathbb{Z}^n…
Rational linear subspaces of hypersurfaces over finite fields
María Inés de Frutos Fernández, Sumita Garai, Kelly Isham +2
Let be a hypersurface of degree defined over a finite field of characteristic . We prove that if , then contains…
An algorithm for counting arcs in higher-dimensional projective space
Kelly Isham
An arc in -dimensional projective space is a set of points so that no lie on a hyperplane. In 1988, Glynn gave a formula to count -arcs in the projective plan…
Lower bounds for the number of subrings in
Kelly Isham
Let be the number of subrings of index in . We show that results of Brakenhoff imply a lower bound for the asymptotic growth of subrings in $\mathbb{Z}^n…
Arithmetic of idempotents in
Kelly Isham, Laura Monroe
Idempotent elements are a well-studied part of ring theory, with several identities of the idempotents in already known. Although the idempotents are not c…
On structures induced by the power sequences of \mathbb{Z}/ m\mathbb{Z}
Kelly Isham, Laura Monroe
In this paper, we explore the structure of in terms of its orbits under modular exponentiation, illustrating this with a sequential power graph that is na…