2 citations · 5 across the 9 of their papers we have counts for
11 papers
Optimal bounds for the colorful fractional Helly theorem
Denys Bulavka, Afshin Goodarzi, Martin Tancer
The well known fractional Helly theorem and colorful Helly theorem can be merged into the so called colorful fractional Helly theorem. It states: For every and every…
Sequentially is a topological property
Afshin Goodarzi
We show that the sequentially condition for simplicial complexes is a topological property. Along the way, we present an elementary proof for the fact that the Serre's cond…
A note on Lefschetz spheres and their relatives
Afshin Goodarzi
Inspired by the works of Adiprasito, Babson, Nevo, and Murai on the -conjecture, we consider different classes of PL-spheres and the relations between them. We focus on a certai…
On Codimension one Embedding of Simplicial Complexes
Anders Björner, Afshin Goodarzi
We study -dimensional simplicial complexes that are PL embeddable in . It is shown that such a complex must satisfy a certain homological condition. The existe…
Dimension filtration, sequential Cohen--Macaulayness and a new polynomial invariant of graded algebras
Afshin Goodarzi
Let $\k$ be a field and let be a standard -graded $\k$-algebra. Using numerical information of some invariants in the primary decomposition of in , namely th…
Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals
Karim A. Adiprasito, Anders Björner, Afshin Goodarzi
A numerical characterization is given of the so-called h-triangles of sequentially Cohen-Macaulay simplicial complexes. This result characterizes the number of faces of various dim…
Connectivity of pseudomanifold graphs from an algebraic point of view
Karim A. Adiprasito, Afshin Goodarzi, Matteo Varbaro
The connectivity of graphs of simplicial and polytopal complexes is a classical subject going back at least to Steinitz, and the topic has since been studied by many authors, inclu…
Clique Vectors of -Connected Chordal Graphs
Afshin Goodarzi
The clique vector of a graph is the sequence in , where is the number of cliques in with vertices and …
Cellular structure for the Herzog--Takayama Resolution
Afshin Goodarzi
Herzog and Takayama constructed explicit resolutions for the class of so called ideals with a regular linear quotient. This class contains all matroidal and stable ideals. The reso…
Convex Hull of Face Vectors of Colored Complexes
Afshin Goodarzi
In this paper we verify a conjecture by Kozlov (Discrete Comput Geom 18 (1997) 421--431), which describes the convex hull of the set of face vectors of -colorable complexes on $…
-Shellability of Discrete Polymatroids
Majid Alizadeh, Afshin Goodarzi, Siamak Yassemi
In this note we show that every discrete polymatroid is -shellable. This gives, in a partial case, a positive answer to a conjecture of Chari and improves a recent result of Sch…