30 citations · 58 across the 12 of their papers we have counts for
13 papers
Characterization of -Milnor numbers of small rank
C-Y. Jean Chan, Thomas Hagedorn, Joel Louwsma +1
The -Milnor number of a polynomial map is a quadratic enrichment of the classical Milnor number, defined as the local -Brouwer degree of the gradient. W…
Transfers and Unstable Degrees in the -Brouwer Degrees Package for Macaulay2
Stephanie Atherton, Somak Dutta, Jordy Lopez Garcia +4
We describe a significant update to the Macaulay2 package A1BrouwerDegrees. We extend several methods in the previous version of the package to the setting of finite étale algebras…
Generalized chip firing and critical groups of arithmetical structures on trees
Kassie Archer, Alexander Diaz-Lopez, Darren Glass +1
Chip firing provides a way to study the sandpile group (also known as the Jacobian) of a graph. We use a generalized version of chip firing to bound the number of invariant factors…
On solutions of in integers of the form
Joel Louwsma
We give an algorithm that produces all solutions of the equation in integers of the form , where is a fixed positive integer that is not a pow…
-Brouwer degrees in Macaulay2
Nikita Borisov, Thomas Brazelton, Frenly Espino +6
We describe the Macaulay2 package "A1BrouwerDegrees" for computing local and global -Brouwer degrees and studying symmetric bilinear forms over the complex numbers, t…
Rational numbers with odd greedy expansion of fixed length
Joel Louwsma, Joseph Martino
Given a positive rational number with odd, its odd greedy expansion starts with the largest odd denominator unit fraction at most , adds the largest odd denominator…
Critical groups of arithmetical structures on star graphs and complete graphs
Kassie Archer, Alexander Diaz-Lopez, Darren Glass +1
An arithmetical structure on a finite, connected graph without loops is an assignment of positive integers to the vertices that satisfies certain conditions. Associated to each of…
Critical groups of arithmetical structures under a generalized star-clique operation
Alexander Diaz-Lopez, Joel Louwsma
An arithmetical structure on a finite, connected graph without loops is given by an assignment of positive integers to the vertices such that, at each vertex, the integer there is…
On Arithmetical Structures on Complete Graphs
Zachary Harris, Joel Louwsma
An arithmetical structure on the complete graph with vertices is given by a collection of positive integers with no common factor each of which divides their sum. We…
Arithmetical structures on bidents
Kassie Archer, Abigail Bishop, Alexander Diaz-Lopez +3
An arithmetical structure on a finite, connected graph is a pair of vectors with positive integer entries for which $(\operatorname{diag}(\mathbf{d})…
Digital Fixed Points, Approximate Fixed Points, and Universal Functions
Laurence Boxer, Ozgur Ege, Ismet Karaca +2
A. Rosenfeld introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous…
Stable commutator length in Baumslag-Solitar groups and quasimorphisms for tree actions
Matt Clay, Max Forester, Joel Louwsma
This paper has two parts, on Baumslag-Solitar groups and on general G-trees. In the first part we establish bounds for stable commutator length (scl) in Baumslag-Solitar groups. Fo…
Immersed surfaces in the modular orbifold
Danny Calegari, Joel Louwsma
A hyperbolic conjugacy class in the modular group PSL(2,Z) corresponds to a closed geodesic in the modular orbifold. Some of these geodesics virtually bound immersed surfaces, and…