37 citations · 54 across the 14 of their papers we have counts for
15 papers
Categorification of characteristic structures
Peter A. Brooksbank, Heiko Dietrich, Joshua Maglione +2
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing o…
Isomorphism invariant metrics
P. A. Brooksbank, J. F. Maglione, E. A. O'Brien +1
Within a category , having objects , it may be instructive to know not only that two objects are non-isomorphic, but also how far from being isomorphic th…
The Poincaré-extended ab-index
Galen Dorpalen-Barry, Joshua Maglione, Christian Stump
Motivated by a conjecture concerning Igusa local zeta functions for intersection posets of hyperplane arrangements, we introduce and study the Poincaré-extended ab-index, which gen…
Smooth cuboids in group theory
Joshua Maglione, Mima Stanojkovski
A smooth cuboid can be identified with a matrix of linear forms, with coefficients in a field , whose determinant describes a smooth cubic in the projective plane. T…
On the geometry of flag Hilbert-Poincaré series for matroids
Lukas Kühne, Joshua Maglione
We extend the definition of coarse flag Hilbert--Poincaré series to matroids; these series arise in the context of local Igusa zeta functions associated to hyperplane arrangements.…
Flag Hilbert-Poincaré series of hyperplane arrangements and their Igusa zeta functions
Joshua Maglione, Christopher Voll
We introduce and study a class of multivariate rational functions associated with hyperplane arrangements, called flag Hilbert-Poincaré series. These series are intimately connecte…
Tensor Isomorphism by conjugacy of Lie algebras
Peter A. Brooksbank, Joshua Maglione, James B. Wilson
We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the Lie algebra of derivations of a tensor to compress the space in which the search takes place…
A spectral theory for transverse tensor operators
Uriya First, Joshua Maglione, James B. Wilson
Tensors are multiway arrays of data, and transverse operators are the operators that change the frame of reference. We develop the spectral theory of transverse tensor operators an…
Exact sequences of inner automorphisms of tensors
Peter A. Brooksbank, Joshua Maglione, James B. Wilson
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences…
Enumerating isoclinism classes of semi-extraspecial groups
Mark L. Lewis, Joshua Maglione
We enumerate the number of isoclinism classes of semi-extraspecial -groups with derived subgroup of order . To do this, we enumerate -orbits of sets of irr…
Compatible filters with isomorphism testing
Joshua Maglione
Like the lower central series of a nilpotent group, filters generalize the connection between nilpotent groups and graded Lie rings. However, unlike the case with the lower central…
Efficient characteristic refinements for finite groups
Joshua Maglione
Filters were introduced by J.B. Wilson in 2013 to generalize work of Lazard with associated graded Lie rings. It holds promise in improving isomorphism tests, but the formulas intr…
A fast isomorphism test for groups of genus 2
Peter A. Brooksbank, Joshua Maglione, James B. Wilson
Motivated by the need for efficient isomorphism tests for finite groups, we present a polynomial-time method for deciding isomorphism within a class of groups that is well-suited t…
Automorphisms of small prime power groups
Joshua Maglione
If is the number of pairwise nonisomorphic groups of order , and is the number of groups of order whose automorphism group is a -group, then, for $…
Longer nilpotent series for classical unipotent subgroups
Joshua Maglione
In studying nilpotent groups, the lower central series and other variations can be used to construct an associated -graded Lie ring, which is a powerful method to ins…