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...

0 downloads 10 Views 363KB Size

Recommend Documents

Jul 9, 2012 - Any two matroids M1 and M2 on a common ground set E have a common .... We end this section with the definition of exchange chains.

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 그 Ç P(E) is the set of independent sets of a matroid iff it ... and so e ∈ 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 − 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 matroid—a se

Feb 23, 2013 - another finitary matroid. Similarly, every bond of an infinite graph would be a circuit in any dual of its cycle matroid—a set of edges minimal with ...

Sep 23, 2014 - have proved this extension with an application in mind: it is used as a tool in the proof ... a lemma that allows us to simplify winning strategies in these games. We ...... in Adv. Math, available at http://arxiv.org/pdf/1204.6294. 24

Jan 23, 2017 - 1Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA 15213. 2Supported by a Mellon Fellowship. 3LIF, Faculté des Sciences de Luminy, Université 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

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

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,

Aug 21, 2018 - related to the arithmetic Gan–Gross–Prasad conjecture for Shimura varieties attached to unitary groups. 1. Introduction. This article is a survey ...

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

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

Jun 14, 2016 - infinite matroids in terms of independent sets, bases, circuits, ... with some new virtual elements corresponding to the edges incident with t in T.

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 v∈VU v . Now, by the infinite circuit elimination axiom (C3

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

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

Oct 24, 2012 - In 1973, Piff [8] gave an improved bound of loglog mn ≤ n − log n + O(1). ... log log mn ≥ n − 3 .... H(XE,r/T) ≤ log |ME\T,r−t| = log(mn−t,r−t + 1).

Mar 5, 2012 - The well-known finite matroid intersection theorem of Edmonds ... set E. A packing for this family consists of a spanning set Sk for each Mk.

Aug 23, 2017 - This paper is a sequel to [Ga1]. We study the semi-infinite category on the Ran version of the affine Grassmannian, and study a particular object ...

Feb 24, 2015 - There are different ways to extend the addition operation from the set ω of ..... brevity, we shall write pw-convex in place of piecewise convex.