This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems. Combinatorial investigations play an important role in this study.

Algorithms in Combinatorial Geometry

Introduction Polytopes Topology and combinatorics of simplicial complexes Commutative and homological algebra of simplicial complexes Cubical complexes Toric and quasitoric manifolds Moment-angle complexes Cohomology of moment-angle complexes and combinatorics of triangulated manifolds Cohomology rings of subspace arrangement complements Bibliography Index.

/pdf/torus-actions-and-their-applications-in-topology-and-36j92o51jp.pdf

Torus Actions and their Applications in Topology and Combinatorics

https://math.mit.edu/~rstan/pubs/pubfiles/46.pdf

The number of faces of a simplicial convex polytope

The double description method is a simple and useful algorithm for enumerating all extreme rays of a general polyhedral cone in ℝd, despite the fact that we can hardly state any interesting theorems on its time and space complexities. In this paper, we reinvestigate this method, introduce some new ideas for efficient implementations, and show some empirical results indicating its practicality in solving highly degenerate problems.

I. G. MacDonald

Papers

Convex polytopes and the upper bound conjecture