Related papers: Reflexive polytopes and discrete polymatroids
We provide a Minkowski sum decomposition of marked chain-order polytopes into building blocks associated to elementary markings and thus give an explicit minimal set of generators of an associated semi-group algebra. We proceed by…
In this paper we introduce toric rings of multicomplexes. We show how to compute the divisor class group and the class of the canonical module when the toric ring is normal. In the special case that the multicomplex is a discrete…
In this paper we investigate the number of integer points lying in dilations of lattice path matroid polytopes. We give a characterization of such points as polygonal paths in the diagram of the lattice path matroid. Furthermore, we prove…
Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many…
We study Dressians of matroids using the initial matroids of Dress and Wenzel. These correspond to cells in regular matroid subdivisions of matroid polytopes. An efficient algorithm for computing Dressians is presented, and its…
The weak-map order on the matroid base polytopes is the partial order defined by inclusion. Lucas proved that the base polytope of no binary matroid includes the base polytope of a connected matroid. A matroid base polytope is said to be…
In this note we study in detail the geometry of eight rational elliptic surfaces naturally associated to the sixteen reflexive polygons. The elliptic fibrations supported by these surfaces correspond under mirror symmetry to the eight…
We give several characterisations of groupoids determined by involutive automorphisms on semilattices of groups.
Polymatroids can be considered as "fractional matroid" where the rank function is not required to be integer valued. Many, but not every notion in matroid terminology translates naturally to polymatroids. Defining cyclic flats of a…
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…
We study the plane automorphisms given by polynomials with certain degree decompositions.
In this paper, we study positroids and its overlap with two classes of matroids: transversal and paving matroids. We exhibit a new class of fundamental transversal matroids and classify the Le-diagram for rank two transversal positroids. We…
Every regular polytope has the remarkable property that it inherits all symmetries of each of its facets. This property distinguishes a natural class of polytopes which are called hereditary. Regular polytopes are by definition hereditary,…
The forms of surjective multiplicative isometries from the Smirnov class on the ball and the polydisk are given.
We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.
In this paper, we obtain a complete classification of compact hyperbolic Coxeter five-dimensional polytopes with nine facets.
Any convex polytope whose combinatorial automorphism group has two orbits on the flags is isomorphic to one whose group of Euclidean symmetries has two orbits on the flags (equivalently, to one whose automorphism group and symmetry group…
This paper is a continuation of our previous work in which we defined the notion of a polytope complex and its $K$-theory. In this paper we produce formulas for the delooping of a simplicial polytope complex and the cofiber of a morphism of…
Hexagonal polyominoes are polyominoes on the honeycomb lattice. We enumerate the symmetry classes of convex hexagonal polyominoes. Here convexity is to be understood as convexity along the three main column directions. We deduce the…
In this survey, we discuss some basic problems concerning random matrices with discrete distributions. Several new results, tools and conjectures will be presented.