14 citations · 109 across the 30 of their papers we have counts for
8 papers · 1 filter
Matroids in toric topology
Anton Ayzenberg, Vladislav Cherepanov
In this paper we study general torus actions on manifolds with isolated fixed points from combinatorial point of view. The main object of study is the poset of face submanifolds of…
Cluster-permutohedra and submanifolds of flag varieties with torus actions
Anton Ayzenberg, Victor Buchstaber
In this paper we describe a relation between the notion of graphicahedron, introduced by Araujo-Pardo, Del R\'ıo-Francos, López-Dudet, Oliveros, and Schulte in 2010, and toric topo…
Dimensions of multi-fan algebras
Anton Ayzenberg
Given an arbitrary non-zero simplicial cycle and a generic vector coloring of its vertices, there is a way to produce a graded Poincare duality algebra associated with these data.…
Volume polynomials and duality algebras of multi-fans
Anton Ayzenberg, Mikiya Masuda
We introduce a theory of volume polynomials and corresponding duality algebras of multi-fans. Any complete simplicial multi-fan determines a volume polynomial whose value…
Buchstaber numbers and classical invariants of simplicial complexes
Anton Ayzenberg
Buchstaber invariant is a numerical characteristic of a simplicial complex, arising from torus actions on moment-angle complexes. In the paper we study the relation between Buchsta…
Simplicial complexes Alexander dual to boundaries of polytopes
Anton Ayzenberg
In the paper we treat Gale diagrams in a combinatorial way. The interpretation allows to describe simplicial complexes which are Alexander dual to boundaries of simplicial polytope…
Moment-angle complexes and polyhedral products for convex polytopes
A. A. Ayzenberg, V. M. Buchstaber
Let P be a convex polytope not simple in general. In the focus of this paper lies a simplicial complex K_P which carries complete information about the combinatorial type of P. In…
The problem of Buchstaber number and its combinatorial aspects
Anton Ayzenberg
For any simplicial complex on m vertices a moment-angle complex Z_K embedded in C^m can be defined. There is a canonical action of a torus T^m on Z_K, but this action fails to be f…