13 citations · 52 across the 13 of their papers we have counts for
17 papers
Permuton limits for some permutations avoiding a single pattern
Kaitlyn Hohmeier, Erik Slivken
Permutons are probability measures on the unit square with uniform marginals that provide a natural way to describe limits of permutations. We are interested in the permuton limits…
Scaling limits of permutations avoiding long decreasing sequences
Christopher Hoffman, Douglas Rizzolo, Erik Slivken
We determine the scaling limit for permutations conditioned to have longest decreasing subsequence of length at most . These permutations are also said to avoid the pattern $(d+…
Almost square permutations are typically square
Jacopo Borga, Enrica Duchi, Erik Slivken
A record in a permutation is a maximum or a minimum, from the left or from the right. The entries of a permutation can be partitioned into two types: the ones that are records are…
Time Scales of the Fredrickson-Andersen Model on Polluted and
Assaf Shapira, Erik Slivken
We study the Kinetically Constrained Model on the polluted square lattice, with two-neighbor constraints. For a quenched polluted environment with low pollution density we give bou…
Square permutations are typically rectangular
Jacopo Borga, Erik Slivken
We describe the limit (for two topologies) of large uniform random square permutations, i.e., permutations where every point is a record. The starting point for all our results is…
Expected size of a tree in the fixed point forest
Samuel Regan, Erik Slivken
We study the local limit of the fixed-point forest, a tree structure associated to a simple sorting algorithm on permutations. This local limit can be viewed as an infinite random…
Maximal spanning time for neighborhood growth on the Hamming plane
Janko Gravner, J. E. Paguyo, Erik Slivken
We consider a long-range growth dynamics on the two-dimensional integer lattice, initialized by a finite set of occupied points. Subsequently, a site becomes occupied if the pa…
Asymptotic distribution of fixed points of pattern-avoiding involutions
Samuel Miner, Douglas Rizzolo, Erik Slivken
For a variety of pattern-avoiding classes, we describe the limiting distribution for the number of fixed points for involutions chosen uniformly at random from that class. In parti…
The bullet problem with discrete speeds
Brittany Dygert, Christoph Kinzel, Jennifer Zhu +3
Bullets are fired, one per second, with independent speeds sampled uniformly from a discrete set. Collisions result in mutual annihilation. We show that the second fastest bullet s…
Neighborhood growth dynamics on the Hamming plane
Janko Gravner, David Sivakoff, Erik Slivken
We initiate the study of general neighborhood growth dynamics on two dimensional Hamming graphs. The decision to add a point is made by counting the currently occupied points on th…
Fixed points of 321-avoiding permutations
Christopher Hoffman, Douglas Rizzolo, Erik Slivken
We describe the distribution of the number and location of the fixed points of permu- tations that avoid the pattern 321 via a bijection with rooted plane trees on n + 1 vertices.…
Local limit of the fixed point forest
Tobias Johnson, Anne Schilling, Erik Slivken
Consider the following partial "sorting algorithm" on permutations: take the first entry of the permutation in one-line notation and insert it into the position of its own value. C…
Pattern-avoiding permutations and Brownian excursion, Part II: Fixed points
Christopher Hoffman, Douglas Rizzolo, Erik Slivken
Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology…
Jigsaw Percolation on Erdos-Renyi Random Graphs
Erik Slivken
We extend the jigsaw percolation model to analyze graphs where both underlying people and puzzle graphs are Erdős-Rényi random graphs. Let and den…
The threshold for jigsaw percolation on random graphs
Béla Bollobás, Oliver Riordan, Erik Slivken +1
Jigsaw percolation is a model for the process of solving puzzles within a social network, which was recently proposed by Brummitt, Chatterjee, Dey and Sivakoff. In the model there…
Bootstrap percolation on the Hamming torus with threshold 2
Erik Slivken
This paper analyzes various questions pertaining to bootstrap percolation on the -dimensional Hamming torus where each node is open with probability and the percolation thre…
Pattern-avoiding permutations and Brownian excursion Part I: Shapes and fluctuations
Christopher Hoffman, Douglas Rizzolo, Erik Slivken
Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology…