Related papers: Equivalence Between Four Models of Associahedra
Coherence in a monoidal category asserts that all morphisms built from structural isomorphisms with a fixed source and target coincide. These structural isomorphisms include, in particular, the associators. Linearly distributive categories…
When the number of non-triangular faces adjacent to a vertex $v$ is less than or equal to three, the vertex $v$ will be called (\emph{combinatorially}) \emph{rigid}. We study the number of rigid vertices and suggest a conjecture on a…
For Hamiltonian circle actions on compact, connected, four-dimensional manifolds, we give a generators and relations description for the even part of the equivariant cohomology, as an algebra over the equivariant cohomology of a point. This…
Polypolyhedra are edge-transitive compounds of polyhedra. In this paper we use group theory to determine the number of distinct polypolyhedra whose symmetry group is any given finite irreducible Coxeter group. We apply this result in order…
This work is part of a series of papers focusing on multipath cohomology of directed graphs. Multipath cohomology is defined as the (poset) homology of the path poset -- i.e., the poset of disjoint simple paths in a graph -- with respect to…
M. Carr and S. Devadoss introduced in [7] the notion of tubing on a finite simple graph $\Gamma$, in the context of configuration spaces on the Hilbert plane. To any finite simple graph $\Gamma$ they associated a finite partially ordered…
We give an explicit subword complex description of the generators of the type cone of the g-vector fan of a finite type cluster algebra with acyclic initial seed. This yields in particular a description of the Newton polytopes of the…
We introduce a new family of graphs, namely, hybrid graphs. There are infinitely many hybrid graphs associated to a single graph. We show that every hybrid graph associated to a given graph is Cohen Macaulay. Furthermore, we show that every…
The complex projective structures considered is this article are compact curves locally modeled on $\mathbb{CP}^1$. To such a geometric object, modulo marked isomorphism, the monodromy map associates an algebraic one: a representation of…
A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. in the context of simplicial (polyhedral) complexes, posets,…
We show that a smaller version of the Kontsevich graph complex spanned by triconnected graphs is quasi-isomorphic to the full Kontsevich graph complex.
We show that there is a collection of subgroups of the mapping class group of a surface such that the associated coset intersection complex is quasi-isometric and homotopy equivalent to the curve complex. Moreover, we prove that these two…
We explain a method for calculating the cohomology of line bundles on a toric variety in terms of the cohomology of certain constructible sheaves on the polytope. We show its effective use by means of some examples.
Many (if not most) of convex polytopes, important for combinatorial and algebraic geometry, are closely related to secondary polytopes of point configurations, or base polytopes of submodular functions, or their numerous variations and…
We describe a graph parametrization of rational quadratic differentials with presence of a simple pole, whose critical trajectories form a network depending on parameters focusing on the network topological jumps. Obtained bifurcation…
In this paper we prove an equivalence theorem originally observed by Robert MacPherson. On one side of the equivalence is the category of cosheaves that are constructible with respect to a locally cone-like stratification. Our…
We describe when two multiprojective bundles (fibre products of projective bundles over the same base) over projective spaces are isomorphic as abstract varieties. We also describe when two relative symmetric powers of projective bundles…
We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. This is done by deriving integral formulae for the Feynman diagrams at tree level and integrands at one…
In this paper, we study the stable homotopy types of $\mathbf{F}^4_{n(2)}$-polyhedra, i.e., $(n-1)$-connected, at most $(n+4)$-dimensional polyhedra with 2-torsion free homologies. We are able to classify the indecomposable…
We consider facet-Hamiltonian cycles of polytopes, defined as cycles in their skeleton such that every facet is visited exactly once. These cycles can be understood as optimal watchman routes that guard the facets of a polytope. We consider…