15 citations · 54 across the 23 of their papers we have counts for
7 papers · 1 filter
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…
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 .
Automorphism groups of finite posets II
Jonathan A. Barmak
We prove that every finite group can be realized as the automorphism group of a poset with points. We also provide bounds for the minimum number of points of a poset wit…
The word problem and the Aharoni-Berger-Ziv conjecture on the connectivity of independence complexes
Jonathan Ariel Barmak
For each finite simple graph , Aharoni, Berger and Ziv consider a recursively defined number which gives a lower bound for the topologica…
Star clusters in independence complexes of graphs
Jonathan Ariel Barmak
We introduce the notion of \textit{star cluster} of a simplex in a simplicial complex. This concept provides a general tool to study the topology of independence complexes of graph…
On Quillen's Theorem A for posets
Jonathan Ariel Barmak
A theorem of McCord of 1966 and Quillen's Theorem A of 1973 provide sufficient conditions for a map between two posets to be a homotopy equivalence at the level of complexes. We gi…