133 citations · 795 across the 60 of their papers we have counts for
6 papers · 1 filter
Gaps problems and frequencies of patches in cut and project sets
Alan Haynes, Henna Koivusalo, Lorenzo Sadun +1
We establish a connection between gaps problems in Diophantine approximation and the frequency spectrum of patches in cut and project sets with special windows. Our theorems provid…
Cohomology of Hierarchical Tilings
Lorenzo Sadun
This is a chapter in an upcoming book on aperiodic order. We go over different versions of tiling cohomology (\v Cech, pattern-equivariant, PV, quotient) with emphasis on the inver…
Conjugacies of model sets
Johannes Kellendonk, Lorenzo Sadun
Let be a model set meeting two simple conditions: (1) the internal space is a product of and a finite group, and (2) the window is a finite union of disjoint poly…
Pattern Equivariant Cohomology and Theorems of Kesten and Oren
Michael Kelly, Lorenzo Sadun
In 1966 Harry Kesten settled the Erd\H os-Szüsz conjecture on the local discrepancy of irrational rotations. His proof made heavy use of continued fractions and Diophantine analysi…
Multipodal Structure and Phase Transitions in Large Constrained Graphs
Richard Kenyon, Charles Radin, Kui Ren +1
We study the asymptotics of large, simple, labeled graphs constrained by the densities of edges and of -star subgraphs, fixed. We prove that under such constraints grap…
The Asymptotics of Large Constrained Graphs
Charles Radin, Kui Ren, Lorenzo Sadun
We show, through local estimates and simulation, that if one constrains simple graphs by their densities of edges and of triangles, then asymptotically (in the nu…