Related papers: Face-subgroups of permutation polytopes

In [7], Higashitani, Kummer, and Micha{\l}ek pose a conjecture about the symmetric edge polytopes of complete multipartite graphs and confirm it for a number of families in the bipartite case. We confirm that conjecture for a number of new…

The $g$-theorem is a momentous result in combinatorics that gives a complete numerical characterization of the face numbers of simplicial convex polytopes. The $g$-conjecture asserts that the same numerical conditions given in the…

We compute the set of facets of the polytope which is the convex hull of the Coxeter groups $\mathsf{F}_4$ or $\mathsf{H}_4$: For the group $\mathsf{F}_4$ we found $2$ orbits of facets which contradicts previous results published in…

We characterize all permutations which realize as the $z$-monodromies of faces in connected simple finite graphs embedded in surfaces whose duals are also simple.

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 polytopes. Using a closely related result of Below, we construct a…

We prove that every finite group is the automorphism group of a finite abstract polytope isomorphic to a face-to-face tessellation of a sphere by topological copies of convex polytopes. We also show that this abstract polytope may be…

We determine all permutation polynomials among several families of polynomials over $\mathbb{F}_{q^3}$ for arbitrary prime powers $q$. We obtain some new families of permutation polynomials over $\mathbb{F}_{q^3}$ with simple coefficients…

In this note we investigate the convex hull of those $n \times n$-permutation matrices that correspond to symmetries of a regular $n$-gon. We give the complete facet description. As an application, we show that this yields a Gorenstein…

A remarkable and important property of face numbers of simplicial polytopes is the generalized lower bound inequality, which says that the $h$-numbers of any simplicial polytope are unimodal. Recently, for balanced simplicial $d$-polytopes,…

The Birkhoff polytope is defined to be the convex hull of permutation matrices, $P_{\sigma}\ \forall \sigma\in S_n$. We define a second-order permutation matrix $P^{[2]}_{\sigma}$ in $\mathbb{R}^{n^2\times n^2}$ corresponding to a…

We obtain a recurrence relation for the f-polynomial of Gelfand-Zetlin polytopes by analyzing geometric properties of a linear projection of the Gelfand-Zetlin polytope onto a cube. We apply this recurrence relation to find explicit…

To each face $\mathcal{F}$ of the coweight polytope $\mathcal{P}_{\mu}$, we associate a subset $\text{Adm}(\mu)_{\mathcal{F}}$ of the $\mu$-admissible set $\text{Adm}(\mu)$, which we refer to as a face of $\text{Adm}(\mu)$. This gives rise…

Enumeration of hypermaps is widely studied in many fields. In particular, enumerating hypermaps with a fixed edge-type according to the number of faces and genus is one topic of great interest. However, it is challenging and explicit…

In an earlier paper, the first two authors defined orientations on hypergraphs. Using this definition we provide an explicit bijection between acyclic orientations in hypergraphs and faces of hypergraphic polytopes. This allows us to obtain…

We extend the notion of a {$p$-permutation equivalence} between two $p$-blocks $A$ and $B$ of finite groups $G$ and $H$, from the definition in [Boltje-Xu 2008] to a virtual $p$-permutation bimodule whose components have twisted diagonal…

The secondary polytope of a point configuration A is a polytope whose face poset is isomorphic to the poset of all regular subdivisions of A. While the vertices of the secondary polytope - corresponding to the triangulations of A - are very…

Let $(V, G)$ be an orthogonal representation of a compact Lie group $G$ with nontrivial copolarity, and $\Sigma$ a fat section of $(V, G)$. If $E$ is a $G$-invariant compact convex set in $V$, then $P=E\cap\Sigma$ is a convex set in…

We present two algorithms that compute the Newton polytope of a polynomial defining a hypersurface H in C^n using numerical computation. The first algorithm assumes that we may only compute values of f - this may occur if f is given as a…

Motivated by the graph associahedron KG, a polytope whose face poset is based on connected subgraphs of G, we consider the notion of associativity and tubes on posets. This leads to a new family of simple convex polytopes obtained by…

We provide asymptotics for the number of faces of a certain family of Hanner polytopes. As a corollary, we come close to saturating the FLM inequality for a certain family of parameters.