Inspired by problems in Private Information Retrieval, we consider the setting where two users need to establish a communication protocol transmit secret without revealing it external observers. This is question of how large linear code can be, when required agree with prescribed on collection coordinate sets. We show efficiency such determined derived matroid underlying code. Furthermore, prov...

In the theory of classical matroids, there are several known equivalent axiomatic systems that define a matroid, which described as matroid cryptomorphisms . A q -matroid is -analogue where subspaces play role subsets in theory. this article we establish -matroids. doing so highlight difference between and its -analogue. We introduce comprehensive set axiom show them existing -matroid. These ax...

As part of the recent developments in infinite matroid theory, there have been a number of conjectures about how standard theorems of finite matroid theory might extend to the infinite setting. These include base packing, base covering, and matroid intersection and union. We show that several of these conjectures are equivalent, so that each gives a perspective on the same central problem of in...

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 generaliz...

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...

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 termin...

The point we try to get across is that the generalization of the counterparts of the matroid theory in Cayley graphs since the matroid theory frequently simplify the graphs and so Cayley graphs. We will show that, for a Cayley graph ΓG, the cutset matroid M ∗(ΓG) is the dual of the circuit matroid M(ΓG). We will also deduce that if Γ ∗ G is an abstract-dual of a Cayley graph Γ, then M(Γ∗ G ) is...

We argue that the chirotope concept of oriented matroid theory may be found in different scenarios of physics, including classical mechanics, quantum mechanics, gauge field theory, p-branes formalism, two time physics and Matrix theory. Our observations may motivate the interest of possible applications of matroid theory in physics.