Related papers: Quotientopes
Flow polytopes of acyclic oriented graphs arise naturally in combinatorial optimization, and the study of their volumes and triangulations has revealed intriguing connections across combinatorics, geometry, algebra, and representation…
The space of configurations of n ordered points in the plane serves as a classifying space for the pure braid group PB_n. Elements of Thompson's group F admit a model similar to braids, except instead of braiding the strands split and…
Spanning trees $T_1,T_2, \dots,T_k$ of $G$ are $k$ completely independent spanning trees if, for any two vertices $u,v\in V(G)$, the paths from $u$ to $v$ in these $k$ trees are pairwise edge-disjoint and internal vertex-disjoint. Hasunuma…
In this paper, we give the Gr\"obner fan and the state polytope of a Specht ideal $I_\lambda$ explicitly. In particular, we show that the state polytope of $I_\lambda$ for a partition $\lambda=(\lambda_1, \ldots, \lambda_m)$ is always a…
Pachner proved that all closed combinatorially equivalent combinatorial manifolds can be transformed into each other by a finite sequence of bistellar moves. We prove an analogue of Pachner's theorem for combinatorial manifolds with a free…
Given a dissimilarity map $\delta$ on finite set $X$, the set of ultrametrics (equidistant tree metrics) which are $l^\infty$-nearest to $\delta$ is a tropical polytope. We give an internal description of this tropical polytope which we use…
A conjecture of Fan and Raspaud [3] asserts that every bridgeless cubic graph con-tains three perfect matchings with empty intersection. Kaiser and Raspaud [6] sug-gested a possible approach to this problem based on the concept of a…
We present a constructive proof of Ky Fan's combinatorial lemma concerning labellings of triangulated spheres. Our construction works for triangulations of $S^n$ that contain a flag of hemispheres. As a consequence, we produce a…
In this paper we classify rank two Fano bundles $\cE$ on Fano manifolds satisfying $H^2(X,\Z)\cong H^4(X,\Z)\cong\Z$. The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization…
A fan is an arc-wise connected hereditarily unicoherent continuum with exactly one branching point. By a result of Borsuk, every fan is a 1-dimensional continuum that can be expressed as the union of a family of arcs, each pair of which…
A fan is a set of edges with a single common endpoint. A graph is fan-crossing if it admits a drawing in the plane so that each edge is crossed by edges of a fan. It is fan-planar if, in addition, the common endpoint is on the same side of…
We examine the lattice of all order congruences of a finite poset from the viewpoint of combinatorial algebraic topology. We will prove that the order complex of the lattice of all nontrivial order congruences (or order-preserving…
We prove that the complex of proper non-trivial non-degenerate subspaces of a finite-dimensional vector space endowed with a non-degenerate sesquilinear form is homotopy equivalent to a wedge of spheres. Additionally, we show that the same…
We study a class of four-dimensional N=1 superconformal field theories obtained by wrapping M5-branes on a Riemann surface with punctures. We identify UV descriptions of four-dimensional SCFTs corresponding to curves with a class of…
A Gorenstein polytope of index r is a lattice polytope whose r-th dilate is a reflexive polytope. These objects are of interest in combinatorial commutative algebra and enumerative combinatorics, and play a crucial role in Batyrev's and…
We introduce the notion of cracked polytope, and - making use of joint work with Coates and Kasprzyk - construct the associated toric variety $X$ as a subvariety of a non-singular toric variety $Y$ under certain conditions. Restricting to…
Suppose that $h$ is an instance of the Gaussian free field (GFF) on a simply connected domain $D \subseteq {\mathbf C}$ and $x,y \in \partial D$ are distinct. Fix $\kappa \in (0,4)$ and for each $\theta \in {\mathbf R}$ let $\eta_\theta$ be…
This note which can be viewed as a complement to Alex Postnikov's paper math.CO/0507163, presents a self-contained overview of basic properties of nested complexes and their two dual polyhedral realizations: as complete simplicial fans, and…
A drawing of a graph is fan-planar if the edges intersecting a common edge $a$ share a vertex $A$ on the same side of $a$. More precisely, orienting $e$ arbitrarily and the other edges towards $A$ results in a consistent orientation of the…
We study two classes of torsion classes which generalize functorially finite torsion classes, that is, semistable torsion classes and morphism torsion classes. Semistable torsion classes are parametrized by the elements in the real…