Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
On analogs of Cremona automorphisms for matroid fans
View through CrossRef
Matroids are combinatorial objects that generalize linear independence. A matroid can be represented geometrically by its Bergman fan and we compare the symmetries of these two objects. Sometimes, the Bergman fan has additional automorphisms, which are related to Cremona transformations in projective space. Their existence depends on a combinatorial property of the matroid, as has been shown by Shaw and Werner, and we study the consequences for the structure of such matroids. This allows us to gain a better understanding of the so-called Cremona group of a matroid and we apply our results to root system matroids.
Title: On analogs of Cremona automorphisms for matroid fans
Description:
Matroids are combinatorial objects that generalize linear independence.
A matroid can be represented geometrically by its Bergman fan and we compare the symmetries of these two objects.
Sometimes, the Bergman fan has additional automorphisms, which are related to Cremona transformations in projective space.
Their existence depends on a combinatorial property of the matroid, as has been shown by Shaw and Werner, and we study the consequences for the structure of such matroids.
This allows us to gain a better understanding of the so-called Cremona group of a matroid and we apply our results to root system matroids.
Related Results
Henry Lives! Learning from Lawson Fandom
Henry Lives! Learning from Lawson Fandom
Since his death in 1922, Henry Lawson’s “spirit” has been kept alive by admirers across Australia. Over the last century, Lawson’s reputation in the academy has fluctuated yet fan ...
Combinatorial Cremona automorphisms and Coxeter arrangement matroids
Combinatorial Cremona automorphisms and Coxeter arrangement matroids
Abstract
We explore birational geometry of matroids by investigating automorphisms of their coarse Bergman fans. Combinatorial Cremona maps provide such automorphisms of ...
Harry Potter and the Fan Fiction Phenomenon
Harry Potter and the Fan Fiction Phenomenon
The Harry Potter (HP) Fan Fiction (FF) phenomenon offers an opportunity to explore the nature of fame and the work of fans (including the second author, a participant observer) in ...
Covering Cycle Matroid
Covering Cycle Matroid
Covering is a type of widespread data representation while covering-based rough sets provide an efficient and systematic theory to deal with this type of data. Matroids are based o...
Groupe de Cremona et espaces hyperboliques
Groupe de Cremona et espaces hyperboliques
Le groupe de Cremona de rang 2 est le groupe des transformations birationnelles du plan projectif. Le but de cette thèse est d'étudier et de construire des espaces hyperboliques su...
Mannityl opine analogs allow isolation of catabolic pathway regulatory mutants
Mannityl opine analogs allow isolation of catabolic pathway regulatory mutants
Five virulent Agrobacterium spp. strains that can catabolize the mannityl opines mannopine (MOP), mannopinic acid ( MOA ), and agropinic acid (AGA) were tested for their ability to...
Faster Matroid Partition Algorithms
Faster Matroid Partition Algorithms
In the matroid partitioning problem, we are given
\(k\)
matroids
\(\mathcal{M}_{1}=(V,\mathcal{I}_{1}...
On certain decompositional properties of von Neumann algebras
On certain decompositional properties of von Neumann algebras
It is well known that if α and β are commuting *-automorphisms of a von Neumann algebra M satisfying the equation α + α-1 = β + β-1 then M can be decomposed into a direct sum of su...