15 citations · 54 across the 23 of their papers we have counts for
26 papers
Topology of medial regime random simplicial complexes
Jonathan Ariel Barmak, Michael Farber
We analyse topology of random simplicial complexes in the medial regime. We show that these complexes are highly connected and have homotopy type of iterated suspensions. One of ou…
Conley index for multivalued maps on finite topological spaces
Jonathan Barmak, Marian Mrozek, Thomas Wanner
We develop Conley's theory for multivalued maps on finite topological spaces. More precisely, for discrete-time dynamical systems generated by the iteration of a multivalued map wh…
Regular and semi-regular representations of groups by posets
Jonathan Ariel Barmak
By a result of Babai, with finitely many exceptions, every group admits a semi-regular poset representation with three orbits, that is, a poset with automorphism group $\te…
Smallest posets with given cyclic automorphism group
Jonathan Ariel Barmak, Agustín Nicolás Barreto
For each we determine the minimum number of points in a poset with cyclic automorphism group of order .
Cop and robber on finite spaces
Jonathan A. Barmak
A cop tries to capture a robber in a topological space being unable to see him. For which spaces does the cop have a strategy which allows him to capture the robber indepen…
Connectivity of ample, conic and random simplicial complexes
Jonathan A. Barmak
A simplicial complex is -conic if every subcomplex of at most vertices is contained in the star of a vertex. A -conic complex is simply connected. We prove that an -co…