Let M be a class of matroids representable over a field F. A matroid N # M stabilizes M if, for any 3-connected matroid M # M, an F-representation of M is uniquely determined by a representation of any one of its N-minors. One of the main theorems of this paper proves that if M is minor-closed and closed under duals, and N is 3-connected, then to show that N is a stabilizer it suffices to check...

This paper is devoted to introduce and investigate some weak forms of fuzzy open mappings, namely fuzzy faintly semi open (fuzzy faintly semi closed), fuzzy faintly preopen (fuzzy faintly preclosed), fuzzy faintly α-open (fuzzy faintly α-closed), fuzzy faintly semi preopen (fuzzy faintly semi preclosed) and fuzzy faintly spopen (fuzzy faintly spclosed) mappings and their fundamental properties ...

The aim of this paper is to introduce the concept of fuzzy generalized closed set and study its properties. Secondly the concept of infra L-fuzzy topological space is introduced. Making use of fuzzy -closed sets and fuzzy -generalized closed sets the concept of fuzzy -generalized continuous mapping is introduced. Lastly the concept of fuzzy generalized closed irresolute map in L-fuzzy topologic...

VCG auctions with reserve prices are practical simple auctions with provably approximately optimal revenue, and have been crucial in the analysis of other appealing auctions. When different reserve prices are applied to different bidders, the auctioneer may choose to apply the reserves either before (eagerly) or after (lazily) the comparison of bids. Both auction forms have been studied in vari...

Bixby and Cunningham showed that a 3-connected binary matroid M is graphic if and only if every element belongs to at most two non-separating cocircuits. Likewise, Lemos showed that such a matroid M is graphic if and only if it has exactly r(M) + 1 nonseparating cocircuits. Hence the presence inM of either an element in at least three non-separating cocircuits, or of at least r(M) + 2 non-separ...

The Orlik-Solomon algebra A of a matroid is isomorphic to the quotient of an exterior algebra E by a defining ideal I . We find an explicit presentation of the annihilator ideal of I or, equivalently, the E-module dual to A. As an application of that we provide a necessary, combinatorial condition for the algebra A to be quadratic. We show that this is stronger than matroid being line-closed th...

This paper introduces a generalization of the matroid operation of ∆ − Y exchange. This new operation, segment-cosegment exchange, replaces a coindependent set of k collinear points in a matroid by an independent set of k points that are collinear in the dual of the resulting matroid. The main theorem of the first half of the paper is that, for every field, or indeed partial field, F, the class...