6 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…
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…
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…