8,255 research outputs found
Searching for a Connection Between Matroid Theory and String Theory
We make a number of observations about matter-ghost string phase, which may
eventually lead to a formal connection between matroid theory and string
theory. In particular, in order to take advantage of the already established
connection between matroid theory and Chern-Simons theory, we propose a
generalization of string theory in terms of some kind of Kahler metric. We show
that this generalization is closely related to the Kahler-Chern-Simons action
due to Nair and Schiff. In addition, we discuss matroid/string connection via
matroid bundles and a Schild type action, and we add new information about the
relationship between matroid theory, D=11 supergravity and Chern-Simons
formalism.Comment: 28 pages, LaTex, section 6 and references adde
Some characteristics of matroids through rough sets
At present, practical application and theoretical discussion of rough sets
are two hot problems in computer science. The core concepts of rough set theory
are upper and lower approximation operators based on equivalence relations.
Matroid, as a branch of mathematics, is a structure that generalizes linear
independence in vector spaces. Further, matroid theory borrows extensively from
the terminology of linear algebra and graph theory. We can combine rough set
theory with matroid theory through using rough sets to study some
characteristics of matroids. In this paper, we apply rough sets to matroids
through defining a family of sets which are constructed from the upper
approximation operator with respect to an equivalence relation. First, we prove
the family of sets satisfies the support set axioms of matroids, and then we
obtain a matroid. We say the matroids induced by the equivalence relation and a
type of matroid, namely support matroid, is induced. Second, through rough
sets, some characteristics of matroids such as independent sets, support sets,
bases, hyperplanes and closed sets are investigated.Comment: 13 page
Phirotopes, Super p-branes and Qubit Theory
The phirotope is a complex generalization of the concept of chirotope in
oriented matroid theory. Our main goal in this work is to establish a link
between phirotopes, super p-branes and qubit theory. For this purpose we first
discuss maximally supersymmetric solutions of 11-dimensional supergravity from
the point of view of the oriented matroid theory. We also clarify a possible
connection between oriented matroid theory and supersymmetry via the
Grassmann-Pl\"ucker relations. These links are in turn useful for explaining
how our approach can be connected with qubit theory.Comment: Latex, 32 pages, improved versio
Fixing numbers for matroids
Motivated by work in graph theory, we define the fixing number for a matroid.
We give upper and lower bounds for fixing numbers for a general matroid in
terms of the size and maximum orbit size (under the action of the matroid
automorphism group). We prove the fixing numbers for the cycle matroid and
bicircular matroid associated with 3-connected graphs are identical. Many of
these results have interpretations through permutation groups, and we make this
connection explicit.Comment: This is a major revision of a previous versio
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