67 citations · 227 across the 19 of their papers we have counts for
21 papers
Asymptotic Betti numbers for hard squares in the homological liquid regime
Hannah Alpert, Matthew Kahle, Robert MacPherson
We study configuration spaces of ordered unit squares in a by rectangle. Our goal is to estimate the Betti numbers for large , , , and . We con…
Topological aspects of Boolean functions
Anders Björner, Mark Goresky, Robert MacPherson
We discuss ways in which tools from topology can be used to derive lower bounds for the circuit complexity of Boolean functions.
Homology of configuration spaces of hard squares in a rectangle
Hannah Alpert, Ulrich Bauer, Matthew Kahle +2
We study ordered configuration spaces of hard squares in a rectangle, a generalization of the well-known "15 Puzzle". Our main interest is in the topolo…
Distribution of Topological Types in Grain-Growth Microstructures
Emanuel A. Lazar, Jeremy K. Mason, Robert D. MacPherson +1
An open question in studying normal grain growth concerns the asymptotic state to which microstructures converge. In particular, the distribution of grain topologies is unknown. We…
Configuration spaces of disks in an infinite strip
Hannah Alpert, Matthew Kahle, Robert MacPherson
We study the topology of the configuration spaces of hard disks of unit diameter in an infinite strip of width . We describe ranges of parameter or "regimes", where…
Roundness of grains in cellular microstructures
Frank H. Lutz, Jeremy K. Mason, Emanuel A. Lazar +1
Many physical systems are composed of polyhedral cells of varying sizes and shapes. These structures are simple in the sense that no more than three faces meet at an edge and no mo…