11 citations · 28 across the 15 of their papers we have counts for
19 papers
Avalanche homology of digraphs via sandpile dynamics
Henri Riihimäki, Jason P. Smith
We introduce avalanche homology as a new (di)graph homology theory, based on the dynamics of the sandpile model. Avalanche homology is the simplicial homology of the avalanche comp…
Multipath complexes of bidirectional polygonal digraphs
Luigi Caputi, Carlo Collari, Jason P. Smith
In this work we study the homotopy type of multipath complexes of bidirectional path graphs and polygons, motivated by works of Vrećica and Živaljević on cycle-free chessboard comp…
Statistical Complexity of Heterogeneous Geometric Networks
Keith Malcolm Smith, Jason P. Smith
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relatio…
On the homotopy type of multipath complexes
Luigi Caputi, Carlo Collari, Sabino Di Trani +1
A multipath in a directed graph is a disjoint union of paths. The multipath complex of a directed graph is the simplicial complex whose faces are the multipaths of ${\tt…
An application of neighbourhoods in digraphs to the classification of binary dynamics
Pedro Conceição, Dejan Govc, Jānis Lazovskis +3
A binary state on a graph means an assignment of binary values to its vertices. For example, if one encodes a network of spiking neurons as a directed graph, then the spikes produc…
Asymptotic Behaviour of the Containment of Certain Mesh Patterns
Dejan Govc, Jason P. Smith
We present some results on the proportion of permutations of length containing certain mesh patterns as grows large, and give exact enumeration results in some cases. In pa…
Complexes of Tournaments, Directionality Filtrations and Persistent Homology
Dejan Govc, Ran Levi, Jason P. Smith
Complete digraphs are referred to in the combinatorics literature as tournaments. We consider a family of semi-simplicial complexes, that we refer to as "tournaplexes", whose simpl…
Computing persistent homology of directed flag complexes
Daniel Luetgehetmann, Dejan Govc, Jason Smith +1
We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrat…
Permutation graphs and the Abelian sandpile model, tiered trees and non-ambiguous binary trees
Mark Dukes, Thomas Selig, Jason P. Smith +1
A permutation graph is a graph whose edges are given by inversions of a permutation. We study the Abelian sandpile model (ASM) on such graphs. We exhibit a bijection between recurr…
The Abelian sandpile model on Ferrers graphs -- A classification of recurrent configurations
Mark Dukes, Thomas Selig, Jason P. Smith +1
We classify all recurrent configurations of the Abelian sandpile model (ASM) on Ferrers graphs. The classification is in terms of decorations of EW-tableaux, which undecorated are…
The poset of graphs ordered by induced containment
Jason P. Smith
We study the poset of all unlabelled graphs, up to isomorphism, with if occurs as an induced subgraph in . We present some general results on the Möbi…
Modular Decomposition of Graphs and the Distance Preserving Property
Emad Zahedi, Jason P. Smith
Given a graph , a subgraph is isometric if for every pair , where is the distance function. A graph is distance preserving (dp) if…
The Poset of Mesh Patterns
Jason P. Smith, Henning Ulfarsson
We introduce the poset of mesh patterns, which generalises the permutation pattern poset. We fully classify the mesh patterns for which the interval [1^\emptyset,m] is non-pure, wh…
EW-tableaux, Le-tableaux, tree-like tableaux and the Abelian sandpile model
Thomas Selig, Jason P. Smith, Einar Steingrimsson
A EW-tableau is a certain 0/1-filling of a Ferrers diagram, corresponding uniquely to an acyclic orientation, with a unique sink, of a certain bipartite graph called a Ferrers grap…
On the Möbius Function and Topology of General Pattern Posets
Jason P. Smith
We introduce a formal definition of a pattern poset which encompasses several previously studied posets in the literature. Using this definition we present some general results on…
On Distance Preserving and Sequentially Distance Preserving Graphs
Jason P. Smith, Emad Zahedi
A graph is an \emph{isometric} subgraph of if , for every pair~. A graph is \emph{distance preserving} if it has an isometric subgraph of e…
A Formula for the Möbius function of the Permutation Poset Based on a Topological Decomposition
Jason P. Smith
We present a two term formula for the Möbius function of intervals in the poset of all permutations, ordered by pattern containment. The first term in this formula is the number of…
Intervals of Permutations with a Fixed Number of Descents are Shellable
Jason P. Smith
The set of all permutations, ordered by pattern containment, is a poset. We present an order isomorphism from the poset of permutations with a fixed number of descents to a certain…
On the Möbius Function of Permutations With One Descent
Jason P Smith
The set of all permutations, ordered by pattern containment, is a poset. We give a formula for the Möbius function of intervals in this poset, for any permutation with…