Oriented matroid structures from realized root systems
نویسندگان
چکیده
منابع مشابه
Oriented matroid systems
The domination invariant has played an important part in reliability theory. While most of the work in this field has been restricted to various types of network system models, many of the results can be generalized to much wider families of systems associated with matroids. A matroid is an ordered pair (F,M), where F is a nonempty finite set and M is a collection of incomparable subsets of F ,...
متن کاملSigned Domination of Oriented Matroid Systems
The domination function has played an important part in reliability theory. While most of the work in this field has been restricted to various types of network system models, many of the results can be generalized to much wider families of systems associated with matroids. Previous papers have explored the relation between undirected network systems and matroids. In this paper the main focus i...
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Several attempts have been made to extend the theory of matroids (here referred to as ordinary or classical matroids) to theories of more general objects, in particular the Coxeter matroids of Borovik, Gelfand and White ([7], first introduced as WP-matroids in [10]), and the ∆-matroids and (equivalent but for notation) symmetric matroids of Bouchet (see, for example, [8]). The special cases of ...
متن کاملMatroid Automorphisms of the F4 Root System
Let F4 be the root system associated with the 24-cell, and let M(F4) be the simple linear dependence matroid corresponding to this root system. We determine the automorphism group of this matroid and compare it to the Coxeter group W for the root system. We find non-geometric automorphisms that preserve the matroid but not the root system.
متن کاملMatroid Automorphisms of the Root System F4
Let F4 be the root system associated with the 24-cell, and let M(F4) be the simple linear dependence matroid corresponding to this root system. We determine the automorphism group of this matroid and compare it to the Coxeter group W for the root system. We find non-geometric automorphisms that preserve the matroid but not the root system.
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2020
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-020-00949-0