11 citations · 16 across the 12 of their papers we have counts for
12 papers
Multi-source invasion percolation on the complete graph
Louigi Addario-Berry, Jordan Barrett
We consider invasion percolation on the randomly-weighted complete graph , started from some number of distinct source vertices. The outcome of the process is a forest…
Finding minimum spanning trees via local improvements
Louigi Addario-Berry, Jordan Barrett, Benoît Corsini
We consider a family of local search algorithms for the minimum-weight spanning tree, indexed by a parameter . One step of the local search corresponds to replacing a connected…
Reverse mathematics of rings
Jordan Mitchell Barrett
Using the tools of reverse mathematics in second-order arithmetic, as developed by Friedman, Simpson, and others, we determine the axioms necessary to develop various topics in com…
Cousin's lemma in second-order arithmetic
Jordan Mitchell Barrett, Rodney G. Downey, Noam Greenberg
Cousin's lemma is a compactness principle that naturally arises when studying the gauge integral, a generalisation of the Lebesgue integral. We study the axiomatic strength of Cous…
Elementary topoi
Jordan Mitchell Barrett
As the prototypical category, has many properties which make it special amongst categories. From the point of view of mathematical logic, one such property is that $…
The reverse mathematics of Cousin's lemma
Jordan Mitchell Barrett
Cousin's lemma is a compactness principle that naturally arises when studying the gauge integral, a generalisation of the Lebesgue integral. We study the axiomatic strength of Cous…
On Ramsey-minimal infinite graphs
Jordan Mitchell Barrett, Valentino Vito
For fixed finite graphs , , a common problem in Ramsey theory is to study graphs such that , i.e. every red-blue coloring of the edges of produces either…
Random tree-weighted graphs
Louigi Addario-Berry, Jordan Barrett
For each , let be a sequence of positive integers with even sum . Let be uniformly dist…
Ramsey theory for layered semigroups
Jordan Mitchell Barrett
We further develop the theory of layered semigroups, as introduced by Farah, Hindman and McLeod, providing a general framework to prove Ramsey statements about such a semigroup …
On functor-quotients and their isomorphism theorems
Jordan Mitchell Barrett, Valentino Vito
The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more gene…
On Rado conditions for nonlinear Diophantine equations
Jordan Mitchell Barrett, Martino Lupini, Joel Moreira
Building on previous work of Di Nasso and Luperi Baglini, we provide general necessary conditions for a Diophantine equation to be partition regular. These conditions are inspired…
The Spread of Voting Attitudes in Social Networks
Jordan Barrett, Christopher Duffy, Richard Nowakowski
The Shapley-Shubik power index is a measure of each voters power in the passage or failure of a vote. We extend this measure to graphs and consider a discrete-time process in which…