12 citations · 35 across the 10 of their papers we have counts for
14 papers
Fundamental groups of small simplicial complexes
Dejan Govc, Wacław Marzantowicz, Łukasz Patryk Michalak +1
The number of nonisomorphic simplicial complexes with up to vertices increases super-exponentially with , which makes exhaustive computation of invariants associated with su…
Equivariant covering type and the number of vertices in equivariant triangulations
Dejan Govc, Waclaw Marzantowicz, Petar Pavesic
We introduce the notion of the \emph{equivariant covering type} of a space on which a finite group acts, and study its properties. The equivariant covering type measures th…
Estimates of covering type and minimal triangulations based on category weight
Dejan Govc, Waclaw Marzantowicz, Petar Pavesic
In a recent publication (D. Govc, W. Marzantowicz, P. Pavesic, Estimates of covering type and the number of vertices of minimal triangulations, Discr. Comp. Geom. 63 (2019), 31-48)…
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…
Computing Homotopy Types of Directed Flag Complexes
Dejan Govc
Combinatorially and stochastically defined simplicial complexes often have the homotopy type of a wedge of spheres. A prominent conjecture of Kahle quantifies this precisely for th…
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…
How many simplices are needed to triangulate a Grassmannian?
Dejan Govc, Wacław Marzantowicz, Petar Pavešić
We compute a lower bound for the number of simplices that are needed to triangulate the Grassmann manifold . In particular, we show that the number of top-dimens…
Persistent Magnitude
Dejan Govc, Richard Hepworth
In this paper we introduce the persistent magnitude, a new numerical invariant of (sufficiently nice) graded persistence modules. It is a weighted and signed count of the bars of t…
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…
Estimates of covering type and the number of vertices of minimal triangulations
Dejan Govc, Wacław Marzantowicz, Petar Pavešić
The covering type of a space is defined as the minimal cardinality of a good cover of a space that is homotopy equivalent to . We derive estimates for the covering type of $…
Unimodal Category and the Monotonicity Conjecture
Dejan Govc
We completely characterize the unimodal category for functions using a decomposition theorem obtained by generalizing the sweeping algorithm of Baryshnik…
An Approximate Nerve Theorem
Dejan Govc, Primoz Skraba
The Nerve Theorem relates the topological type of a suitably nice space with the nerve of a good cover of that space. It has many variants, such as to consider acyclic covers and n…
On the definition of homological critical value
Dejan Govc
We point out that there is a problem with the definition of homological critical value (as defined in the widely cited paper \cite{stability} by Cohen-Steiner, Edelsbrunner and Har…