4 citations · 6 across the 16 of their papers we have counts for
26 papers
Nonabelian partial difference sets constructed using abelian techniques
James Davis, John Polhill, Ken Smith +1
A -partial difference set (PDS) is a subset of a group such that , , and every nonidentity element of can be written in either or…
Genuinely nonabelian partial difference sets
John Polhill, James Davis, Ken Smith +1
Strongly regular graphs (SRGs) provide a fertile area of exploration in algebraic combinatorics, integrating techniques in graph theory, linear algebra, group theory, finite fields…
Null ideals of sets of similar matrices with irreducible characteristic polynomial
Eric Swartz, Nicholas J. Werner
Let be a field and the ring of matrices over . Given a subset of , the null ideal of is the set of all polynomials with coefficient…
Cliques and independent subgroups of the Birkhoff polytope graph
Zejun Huang, Chi-Kwong Li, Eric Swartz +1
The Birkhoff polytope is the polytope of doubly stochastic matrices of order . The Birkhoff polytope graph is the skeleton of ; it is the Cayley graph whose…
A new infinite family of -elementary rings
Eric Swartz, Nicholas J. Werner
A cover of an associative (not necessarily commutative nor unital) ring is a collection of proper subrings of whose set-theoretic union equals . If such a cover exists,…
Locally s-arc-transitive graphs arising from product action
Michael Giudici, Eric Swartz
We study locally -arc-transitive graphs arising from the quasiprimitive product action (PA). We prove that, for any locally -arc-transitive graph with acting quasipri…
The covering numbers of rings
Eric Swartz, Nicholas J. Werner
A cover of an associative (not necessarily commutative nor unital) ring is a collection of proper subrings of whose set-theoretic union equals . If such a cover exists,…
Covering numbers of commutative rings
Eric Swartz, Nicholas J. Werner
A cover of a unital, associative (not necessarily commutative) ring is a collection of proper subrings of whose set-theoretic union equals . If such a cover exists, then…
Restrictions on parameters of partial difference sets in nonabelian groups
Eric Swartz, Gabrielle Tauscheck
A partial difference set in a finite group satisfying and corresponds to an undirected strongly regular Cayley graph . While the c…
Homomorphisms of matrix algebras and constructions of Butson-Hadamard matrices
Padraig O Cathain, Eric Swartz
An matrix is Butson-Hadamard if its entries are roots of unity and it satisfies . Write for the set of such matrices. Suppo…
Fuchs' problem for 2-groups
Eric Swartz, Nicholas J. Werner
Nearly years ago, László Fuchs posed the problem of determining which groups can be realized as the group of units of a commutative ring. To date, the question remains open, a…
A classification of finite locally 2-transitive generalized quadrangles
John Bamberg, Cai Heng Li, Eric Swartz
Ostrom and Wagner (1959) proved that if the automorphism group of a finite projective plane acts -transitively on the points of , then is isomorphic to the Desarg…
On prime order automorphisms of generalized quadrangles
Santana F. Afton, Eric Swartz
In this paper, we study prime order automorphisms of generalized quadrangles. We show that, if is a thick generalized quadrangle of order , where and $…
Spectra of Hadamard matrices
Ronan Egan, Padraig O Cathain, Eric Swartz
A Butson Hadamard matrix has entries in the kth roots of unity, and satisfies the matrix equation . We write for the set of such matrice…
On integers that are covering numbers of groups
Martino Garonzi, Luise-Charlotte Kappe, Eric Swartz
The covering number of a group , denoted by , is the size of a minimal collection of proper subgroups of whose union is . We investigate which integers are covering…
Transitive PSL(2,11)-invariant k-arcs in PG(4,q)
Torger Olson, Eric Swartz
A \textit{k}-arc in the projective space is a set of projective points such that no subcollection of points is contained in a hyperplane. In this paper, w…
On generalized quadrangles with a point regular group of automorphisms
Eric Swartz
A generalized quadrangle is a point-line incidence geometry such that any two points lie on at most one line and, given a line and a point not incident with , ther…
On the number of reachable pairs in a digraph
Eric Swartz, Nicholas J. Werner
A pair of (not necessarily distinct) vertices in a directed graph is called a reachable pair if there exists a directed path from to . We define the weight of $…
Improved User-Private Information Retrieval via Finite Geometry
Oliver Gnilke, Marcus Greferath, Camilla Hollanti +3
In a User-Private Information Retrieval (UPIR) scheme, a set of users collaborate to retrieve files from a database without revealing to observers which participant in the scheme r…
Graphs that contain multiply transitive matchings
Alex Schaefer, Eric Swartz
Let be a finite, undirected, connected, simple graph. We say that a matching is a \textit{permutable -matching} if contains edges and the sub…
The circular altitude of a graph
John Bamberg, Brian Corr, Alice Devillers +3
In this paper we investigate a parameter of graphs, called the circular altitude, introduced by Peter Cameron. We show that the circular altitude provides a lower bound on the circ…
A classification of finite antiflag-transitive generalized quadrangles
John Bamberg, Cai Heng Li, Eric Swartz
A generalized quadrangle is a point-line incidence geometry such that: (i) any two points lie on at most one line, and (ii) given a line and a point not in…
A note on relative hemisystems of Hermitian generalised quadrangles
John Bamberg, Melissa Lee, Eric Swartz
In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space , unifying all known infinite familie…
On the covering number of symmetric groups of even degree
Eric Swartz
If a group is the union of proper subgroups , we say that the collection is a cover of , and the size of a minimal cover (supposing on…