# Matroids with an infinite circuit-cocircuit intersection

Feb 28, 2012 - intersection, consisting of the dotted bold edges, is evidently infinite. ..... http://diestel-graph-theory.com/index.html. [8] A. Dres...

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Apr 24, 2014 - better behaved subclass of infinite matroids, called tame matroids. This class includes all finitary matroids and all the other motivating examples of infinite matroids but is easier to work with than the class of infinite matroids in

Dec 17, 2012 - and topological cycle matroids of a given graph each have a unique signing. ... A set system ê·¸ Ã P(E) is the set of independent sets of a matroid iff it ... and so e â bf . The converse implication is the dual statement of the abo

Aug 30, 2016 - linear spaces, which is an actual geometric object, to which an intersection prod- uct can be applied. Well-definedness then follows from the distributivity of the intersection product. We now summarize our main results: Theorem. With

Aug 30, 2016 - show that it is also the number of nested matroids of rank r+1 on n labeled elements. ... They encode the full lattice of flats and nested matroids can thus ..... where for each chain C we define. (vM )C = 1, if C is a chain of flats i

Jul 10, 2012 - sets missing exactly k â 1 points; since these sets are infinite, however, they cannot be the circuits of another finitary matroid. Similarly, every bond of an infinite graph would be a circuit in any dual of its cycle matroidâa se

Jan 23, 2017 - 1Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA 15213. 2Supported by a Mellon Fellowship. 3LIF, FacultÃ© des Sciences de Luminy, UniversitÃ© de Marseille, France. 4Supported by NSF grant CMMI0653419, ONR grant N0

Sep 15, 2013 - Abstract. An infinite matroid is graphic if all of its finite minors are graphic and the intersection of any circuit with any cocircuit is finite. We show that a matroid is graphic if and only if it can be represented by a graph-like t

Dec 2, 2014 - each edge of G is contained in precisely one Pt. We call the subgraphs Pt, the ..... Then f meets an edge e in an interior point if and only if it traverses this edge precisely once. The set of those edges e is called the edge set of f,

Jan 25, 2013 - infinite graphs: Two finite graphs are dual if and only if their cycle matroids are dual to each other. In the infinite case, the situation is no longer that easy since there are at least two different cycle matroids associated to an i

Sep 30, 2015 - Mathematics and Computer Science (DIMACOS'11) organized by A. ...... Mathematics & Statistics Department, University of Calgary, Calgary, ...

Jun 5, 2015 - or circuits or cocircuits, and the edges of T correspond to certain nested .... Two k-separations (A, Ae) and (B,Be) of M are said to be nested if one of the ..... Put VM = J vâVU v . Now, by the infinite circuit elimination axiom (C3

Mar 12, 2015 - 4. Let now Î be a finitely generated group. We will fix a finite symmet- ric generating set S of Î, and study partial tiles in the Cayley graph of Î w.r.t. the left invariant ... write Heesch(K) = N if N is the maximal non-negative

Dec 13, 2013 - Section 7 contains a detailed treatment of small determinantal matroids, for which we .... by the data D and the associated construction process, as compared to the matroid alone which has no structure or ...... The other family of exa

In this paper we examine the effect of removing cocircuits from regular matroids and we focus on the case in which such a removal always results in a graphic matroid. The first main result, given in section 3, is that a regular matroid with graphic c

Abstract. A generalized Kadomtsev-Petviashvili equation, describing water waves in oceans of varying depth, density and vorticity is discussed. A priori, it involves. 9 arbitrary functions of one, or two variables. The conditions are determined under

Sep 29, 2017 - arXiv:1709.10258v1 [cs.CC] 29 Sep 2017. Recognizing Matroids. Brahim Chaourar. Department of Mathematics and Statistics,. Al Imam University (IMSIU). P.O. Box 90950, Riyadh 11623, Saudi Arabia. Correspondence address: P. O. Box 287574,

our basic understanding of how nature is structured. This ongoing change of cosmological paradigms from a âsmallâ finite cosmos to an infinite fractal cosmos began about three decades ago and is in full swing at present. The short version of what

Feb 3, 2009 - a freest splice; we call this matroid the free splice of M and N and denote it by. M â¶ N. If A â© B = â, then the free ... free splice as a particular Higgs lift, we show that it is indeed the freest splice, we show that it preserv

Feb 3, 2016 - show that delta-matroids arise as the natural extension of graphic matroids to .... Perhaps one of the most spectacular illustrations of the effect of ...

Mar 15, 2011 - Department of Mathematics. Brooklyn College, City University of New York. Brooklyn, NY 11210 [email protected] Manoel Lemos 2. Departamento de Matematica ... A matroid is internally k-connected if it is k-connected and has no

Jan 13, 2015 - R3 for origin-symmetric axially convex bodies of revolution in [21]. In con- nection with the Busemann-Petty problem in Rn, bodies of revolution were used by A. Giannopoulos in [17] to supply a negative answer for n â¥ 7, by M. Papadi

Jun 27, 2016 - Abstract. A laminar family is a collection A of subsets of a set. E such that, for any two intersecting sets, one is contained in the other. For a capacity function c on A, let I be {I : |I â© A| â¤ c(A) for all A â A}. Then I is t

Apr 9, 2017 - 0.000201. Thus, (cj â c)3n > 2/9. So if h â¤ 2/9 the inequalities (1) and (2) are satisfied. Further we show that if h â¤ 2/9, the system S satisfies open set condition(OSC) and one point intersection property and the attractor K is

Apr 9, 2017 - ous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where elements arrive one-by-one in random order, revealing a weight upon arrival. The decision whether