32 citations · 122 across the 43 of their papers we have counts for
4 papers · 1 filter
Derived subdivisions make every PL sphere polytopal
Karim A. Adiprasito, Ivan Izmestiev
We give a simple proof that some iterated derived subdivision of every PL sphere is combinatorially equivalent to the boundary of a simplicial polytope, thereby resolving a problem…
An Alexander-type duality for valuations
Karim Adiprasito, Raman Sanyal
We prove an Alexander-type duality for valuations for certain subcomplexes in the boundary of polyhedra. These strengthen and simplify results of Stanley (1974) and Miller-Reiner (…
The Hirsch conjecture holds for normal flag complexes
Karim Alexander Adiprasito, Bruno Benedetti
Using an intuition from metric geometry, we prove that any flag and normal simplicial complex satisfies the non-revisiting path conjecture. As a consequence, the diameter of its fa…
A universality theorem for projectively unique polytopes and a conjecture of Shephard
Karim Alexander Adiprasito, Arnau Padrol
We prove that every polytope described by algebraic coordinates is the face of a projectively unique polytope. This provides a universality property for projectively unique polytop…