32 citations · 122 across the 43 of their papers we have counts for
32 papers · 1 filter
Lattice polytopes and semigroup algebras: Generic Lefschetz properties and Parseval-Rayleigh identities
Karim Alexander Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou
We study semigroup algebras associated to lattice polytopes. We begin by generalizing and refining work of Hochster, and describe the volume maps of these algebras, that is, their…
Beyond positivity in Ehrhart Theory
Karim Alexander Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou +1
We study semigroup algebras arising from lattice polytopes, compute their volume polynomials (particularizing work of Hochster), and establish strong Lefschetz properties (generali…
Anisotropy, biased pairings, and the Lefschetz property for pseudomanifolds and cycles
Karim Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou
We prove the hard Lefschetz property for pseudomanifolds and cycles in any characteristic with respect to an appropriate Artinian reduction. The proof is a combination of Adiprasit…
A complete characterization of -pairs of 6-polytopes
Karim Adiprasito, Rémi Cocou Avohou
We completely characterize the first two entries, namely the -vector pairs, for -dimension polytopes. We also find the characterization for -dimension polytopes w…
A subexponential size triangulation of
Karim Adiprasito, Sergey Avvakumov, Roman Karasev
We address a long-standing and long-investigated problem in combinatorial topology, and break the exponential barrier for triangulations of real projective space, constructing a tr…
The Partition Complex: an invitation to combinatorial commutative algebra
Karim Adiprasito, Geva Yashfe
We provide a new foundation for combinatorial commutative algebra and Stanley-Reisner theory using the partition complex introduced in [Adi18]. One of the main advantages is that i…
On the realization space of the cube
Karim Adiprasito, Daniel Kalmanovich, Eran Nevo
We consider the realization space of the -dimensional cube, and show that any two realizations are connected by a finite sequence of projective transformations and normal transf…
Unstable blueprints can be shared
Karim Adiprasito
This expository note illustrates toric perturbation and biased pairing theory to show that Artinian reductions of face rings of -spheres that do not satisfy the Lefschetz proper…
FAQ on the g-theorem and the hard Lefschetz theorem for face rings
Karim Adiprasito
This short review is the result of a minicourse at the Sapienza University of Rome the author gave about the proof of the -theorem. We review the hard Lefschetz theorem for simp…
The Hard Lefschetz Theorem for PL spheres
Karim Adiprasito, Johanna K. Steinmeyer
We provide a simpler proof of the hard Lefschetz Theorem for face rings of PL spheres: While the algebraic theory remains the same, we replace the geometric constructions by Pachne…
Combinatorial Lefschetz theorems beyond positivity
Karim Adiprasito
Consider a simplicial complex that allows for an embedding into . How many faces of dimension or higher can it have? How dense can they be? This basic q…
Rigidity with few locations
Karim Adiprasito, Eran Nevo
Graphs triangulating the -sphere are generically rigid in -space, due to Gluck-Dehn-Alexandrov-Cauchy. We show there is a \emph{finite} subset in -space so that the ve…
QGLBT for polytopes
Karim Adiprasito, Mikhail Burens, Eran Nevo
We extend the assertion of the Generalized Lower Bound Theorem (GLBT) to general polytopes under the assumption that their low dimensional skeleton is simplicial, with partial resu…
Lefschetz and Lower Bound theorems for Minkowski sums
Karim Adiprasito
This note provides a Lefschetz theorem for Minkowski sums of polytopes, and conclude lower bound theorems for Minkowski sums of polytopes. It is written as an appendix to arXiv:140…
A Cheeger-type exponential bound for the number of triangulated manifolds
Karim Adiprasito, Bruno Benedetti
In terms of the number of triangles, it is known that there are more than exponentially many triangulations of surfaces, but only exponentially many triangulations of surfaces with…
Barycentric subdivisions of convex complexes are collapsible
Karim Adiprasito, Bruno Benedetti
A classical question in PL topology, asked among others by Hudson, Lickorish, and Kirby, is whether every linear subdivision of the d-simplex is simplicially collapsible. The answe…
Colorful simplicial depth, Minkowski sums, and generalized Gale transforms
Karim Adiprasito, Philip Brinkmann, Arnau Padrol +3
The colorful simplicial depth of a collection of d+1 finite sets of points in Euclidean d-space is the number of choices of a point from each set such that the origin is contained…
Whitney numbers of arrangements via measure concentration of intrinsic volumes
Karim A. Adiprasito, Raman Sanyal
We verify the Rota-Heron-Welsh conjecture for matroids realizable as c-arrangements: the coefficients of the characteristic polynomial of the associated matroid are log-concave. Th…
On Betti numbers of flag complexes with forbidden induced subgraphs
Karim Adiprasito, Eran Nevo, Martin Tancer
We analyze the asymptotic extremal growth rate of the Betti numbers of clique complexes of graphs on n vertices not containing a fixed forbidden induced subgraph H. In particular,…
Hodge Theory for Combinatorial Geometries
Karim Adiprasito, June Huh, Eric Katz
We prove the hard Lefschetz theorem and the Hodge-Riemann relations for a commutative ring associated to an arbitrary matroid M. We use the Hodge-Riemann relations to resolve a con…
Toric chordality
Karim Adiprasito
We study the geometric change of Chow cohomology classes in projective toric varieties under the Weil-McMullen dual of the intersection product with a Lefschetz element. Based on t…
Higher chordality: From graphs to complexes
Karim A. Adiprasito, Eran Nevo, Jose A. Samper
We generalize the fundamental graph-theoretic notion of chordality for higher dimensional simplicial complexes by putting it into a proper context within homology theory. We genera…
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…