32 citations · 122 across the 43 of their papers we have counts for
8 papers · 1 filter
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…
Universality theorems for inscribed polytopes and Delaunay triangulations
Karim A. Adiprasito, Arnau Padrol, Louis Theran
We prove that every primary basic semialgebraic set is homotopy equivalent to the set of inscribed realizations (up to Möbius transformation) of a polytope. If the semialgebraic se…
Relative Stanley-Reisner theory and Upper Bound Theorems for Minkowski sums
Karim Adiprasito, Raman Sanyal
In this paper we settle long-standing questions regarding the combinatorial complexity of Minkowski sums of polytopes: We give a tight upper bound for the number of faces of a Mink…
Extremal examples of collapsible complexes and random discrete Morse theory
Karim A. Adiprasito, Bruno Benedetti, Frank H. Lutz
We present extremal constructions connected with the property of simplicial collapsibility. (1) For each , there are collapsible (and shellable) simplicial -complexes w…
Methods from Differential Geometry in Polytope Theory
Karim Alexander Adiprasito
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in c…
Linear embeddings of contractible and collapsible complexes
Karim A. Adiprasito, Bruno Benedetti
(1) We show that if a presentation of the trivial group is "hard to trivialize", in the sense that lots of Tietze moves are necessary to transform it into the trivial presentation,…
The universality theorem for neighborly polytopes
Karim A. Adiprasito, Arnau Padrol
In this note, we prove that every open primary basic semialgebraic set is stably equivalent to the realization space of an even-dimensional neighborly polytope. This in particular…
Filtered geometric lattices and Lefschetz Section Theorems over the tropical semiring
Karim Alexander Adiprasito, Anders Björner
The purpose of this paper is to establish analogues of the classical Lefschetz Section Theorem for smooth tropical varieties. More precisely, we prove tropical analogues of the sec…