Coxeter matroid polytopes

1997 ◽  
Vol 1 (1) ◽  
pp. 123-134 ◽  
Author(s):  
Alexandre V. Borovik ◽  
Israel M. Gelfand ◽  
Neil White
Keyword(s):  
Coxeter Matroid ◽  
Matroid Polytopes

scholarly journals On the Ehrhart Polynomial of Minimal Matroids

2021 ◽  
Author(s):  
Luis Ferroni
Keyword(s):  
Ehrhart Polynomial ◽  
Matroid Polytopes ◽  
Connected Matroid ◽  
Fixed Rank

AbstractWe provide a formula for the Ehrhart polynomial of the connected matroid of size n and rank k with the least number of bases, also known as a minimal matroid. We prove that their polytopes are Ehrhart positive and $$h^*$$ h ∗ -real-rooted (and hence unimodal). We prove that the operation of circuit-hyperplane relaxation relates minimal matroids and matroid polytopes subdivisions, and also preserves Ehrhart positivity. We state two conjectures: that indeed all matroids are $$h^*$$ h ∗ -real-rooted, and that the coefficients of the Ehrhart polynomial of a connected matroid of fixed rank and cardinality are bounded by those of the corresponding minimal matroid and the corresponding uniform matroid.

scholarly journals Equifacetted 3-spheres as topes of nonpolytopal matroid polytopes

1995 ◽  
Vol 13 (3-4) ◽  
pp. 347-361 ◽  
Author(s):  
J. Bokowski ◽  
P. Schuchert
Keyword(s):  
Matroid Polytopes

scholarly journals Weak Generalized Lifting Property, Bruhat Intervals, and Coxeter Matroids

2020 ◽  
Author(s):  
Fabrizio Caselli ◽  
Michele D’Adderio ◽  
Mario Marietti
Keyword(s):  
Coxeter Group ◽  
Coxeter Groups ◽  
Combinatorial Properties ◽  
Coxeter Matroid ◽  
Finite Coxeter Group ◽  
Bruhat Intervals

Abstract We provide a weaker version of the generalized lifting property that holds in complete generality for all Coxeter groups, and we use it to show that every parabolic Bruhat interval of a finite Coxeter group is a Coxeter matroid. We also describe some combinatorial properties of the associated polytopes.

scholarly journals Facial structures of lattice path matroid polytopes

2020 ◽  
Vol 343 (1) ◽  
pp. 111628
Author(s):  
Suhyung An ◽  
JiYoon Jung ◽  
Sangwook Kim
Keyword(s):  
Lattice Path ◽  
Matroid Polytopes

scholarly journals Ehrhart Polynomials of Matroid Polytopes and Polymatroids

2008 ◽  
Vol 42 (4) ◽  
pp. 703-704
Author(s):  
Jesús A. De Loera ◽  
David C. Haws ◽  
Matthias Köppe
Keyword(s):  
Ehrhart Polynomials ◽  
Matroid Polytopes

scholarly journals Valuations for Matroid Polytope Subdivisions

2010 ◽  
Vol 62 (6) ◽  
pp. 1228-1245 ◽  
Author(s):  
Federico Ardila ◽  
Alex Fink ◽  
Felipe Rincón
Keyword(s):  
Matroid Polytope ◽  
Matroid Polytopes

AbstractWe prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.

scholarly journals Matroid Polytopes and their Volumes

2009 ◽  
Vol 43 (4) ◽  
pp. 841-854 ◽  
Author(s):  
Federico Ardila ◽  
Carolina Benedetti ◽  
Jeffrey Doker
Keyword(s):  
Matroid Polytopes

scholarly journals Isotropical Linear Spaces and Valuated Delta-Matroids

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Felipe Rincón
Keyword(s):  
Symmetric Matrix ◽  
Combinatorial Theory ◽  
Linear Spaces ◽  
Dimensional Vector Space ◽  
Type D ◽  
Matroid Polytopes ◽  
International Audience ◽  
Isotropic Subspaces ◽  
Tropical Basis ◽  
Espace Vectoriel

International audience The spinor variety is cut out by the quadratic Wick relations among the principal Pfaffians of an $n \times n$ skew-symmetric matrix. Its points correspond to $n$-dimensional isotropic subspaces of a $2n$-dimensional vector space. In this paper we tropicalize this picture, and we develop a combinatorial theory of tropical Wick vectors and tropical linear spaces that are tropically isotropic. We characterize tropical Wick vectors in terms of subdivisions of Delta-matroid polytopes, and we examine to what extent the Wick relations form a tropical basis. Our theory generalizes several results for tropical linear spaces and valuated matroids to the class of Coxeter matroids of type $D$. La variété spinorielle est decoupée par les relations quadratiques de Wick parmi les Pfaffiens principaux d'une matrice antisymétrique $n \times n$. Ses points correspondent aux sous-espaces isotropes à $n$ dimensions d'un espace vectoriel de dimension $2n$. Dans cet article nous tropicalisons cette description, et nous développons une théorie combinatoire de vecteurs tropicaux de Wick et d'espaces linéaires tropicaux qui sont tropicalement isotropes. Nous caractérisons des vecteurs tropicaux de Wick en termes de subdivisions des polytopes Delta-matroïde, et nous étudions dans quelle mesure les relations de Wick forment une base tropicale. Notre théorie généralise plusieurs résultats pour les espaces linéaires tropicaux et évaluait des matroïdes à la classe des matroïdes de Coxeter du type $D$.

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