10 citations · 31 across the 10 of their papers we have counts for
10 papers
On the tails of FI-modules
Peter Patzt, John D. Wiltshire-Gordon
We study the end-behavior of integer-valued FI-modules. Our first result describes the high degrees of an FI-module in terms of newly defined tail invariants. Our main result provi…
Configuration space in a product
John D. Wiltshire-Gordon
Given a finite graph G and a topological space Z, the graphical configuration space Conf(G, Z) is the space of functions V(G) -> Z so that adjacent vertices map to distinct points.…
On computing the eventual behavior of an FI-module over the rational numbers
John D. Wiltshire-Gordon
We give a formula for the eventual multiplicities of irreducible representations appearing in a finitely-presented FI-module over the rational numbers. The result relies on structu…
Models for Configuration Space in a Simplicial Complex
John D. Wiltshire-Gordon
We produce combinatorial models for configuration space in a simplicial complex, and for configurations near a single point ("local configuration space.") The model for local confi…
Specht Polytopes and Specht Matroids
John D. Wiltshire-Gordon, Alexander Woo, Magdalena Zajaczkowska
The generators of the classical Specht module satisfy intricate relations. We introduce the Specht matroid, which keeps track of these relations, and the Specht polytope, which als…
Categories of Dimension Zero
John D. Wiltshire-Gordon
If D is a category and k is a commutative ring, the functors from D to k-Mod can be thought of as representations of D. By definition, D is dimension zero over k if its finitely ge…
Algebraic structures on cohomology of configuration spaces of manifolds with flows
Jordan S. Ellenberg, John D. Wiltshire-Gordon
Let PConf^n M be the configuration space of ordered n-tuples of distinct points on a smooth manifold M admitting a nowhere-vanishing vector field. We show that the ith cohomology g…
Uniformly Presented Vector Spaces
John D. Wiltshire-Gordon
Gaussian elimination answers any question about a finitely presented vector space. However, a "uniform family" of such presentations--given as generic relations among an unspecifie…
Word-Induced Measures on Compact Groups
Gene S. Kopp, John D. Wiltshire-Gordon
Consider a group word w in n letters. For a compact group G, w induces a map G^n \rightarrow G$ and thus a pushforward measure μ_w on G from the Haar measure on G^n. We associate t…
Robust Coin Flipping
Gene S. Kopp, John D. Wiltshire-Gordon
Alice seeks an information-theoretically secure source of private random data. Unfortunately, she lacks a personal source and must use remote sources controlled by other parties. A…