Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 30 for “"Matroids."”.
-
Regular Round Matroids
… subsets of <em>E</em> to be independent. Some matroids, called regular matroids, have the property that all elements in their ground set can be represented by vectors over any field. A matroid is called round if its dual has no two disjoint minimal dependent sets. Roundness is an important …
-
Matchings, matroids and submodular functions
… independent set for two so-called "linear" matroids. Our algorithm has running time O(nrw-1) for matroids with n elements and rank r. This is the best-known running time of any linear matroid intersection algorithm. We also consider lower bounds on the efficiency of matroid intersection …
-
Unavoidable minors in graphs and matroids
… parallel minors for 3-connected regular matroids, which combines the results for unavoidable series and parallel minors for graphs with Seymour's decomposition theorem for regular matroids.
-
Theory and applications of freedom in matroids
… flats of M*. If ζ(M) is the set of integer polymatroids with underlying matroid structure M, then we show that for any cell e of M ǁ e ǁ= \frac{max\ f \ (e)}{f\in\zeta} We look at freedom in binary matroids and show that for a connected binary matroid M, ǁ e ǁ is the number of connected …
-
Applications of Powerset Operators, Especially to Matroids
<p>Let \(\mathcal{V}\) denote a vector space over an arbitrary field with an inner product. For any collection \(\mathcal{S}\) of vectors from \(\mathcal{V}\) the collection of all vectors orthogonal to each vector in \(\mathcal{S}\) is a subspace, denoted as \(\mathcal{S}^{\perp_v}\) and called …
-
On Binary And Regular Matroids Without Small Minors
… consist of excluded-minor results for Binary Matroids and excluded-minor results for Regular Matroids. Structural theorems on the relationship between minors and k-sums of matroids are developed here in order to provide some of these characterizations. Chapter 2 of the dissertation contains …
-
Bicircular Matroids with Circuits of at Most Two Sizes
… that Murty in his paper titled, Equicardinal Matroids and Finite Geometries in 1968, was the first to study matroids with all hyperplanes having the same size. Murty called such a matroid an ``Equicardinal Matroid''. Young renamed such a matroid a ``Matroid Design''. Further work on …
-
The structure of 4-separations in 4-connected matroids
… petals. Specializing to the case of 4-connected matroids, we give a new notion of equivalence of 4-separations that we show will be needed to describe a tree decomposition for 4-connected matroids. Finally, we characterize all internally 4-connected binary matroids M with the property that the …
-
Algebraic dependence testing in the perspective of algebraic matroids
… algebraic independence gives rise to a class of matroids, this relation is rarely discussed in the computer science literature. We then describe the previous results on algebraic dependence testing in the perspective of algebraic matroids, and hope to provide powerful tools and novel directions …
-
Enumerative and algebraic aspects of matroids and hyperplane arrangements
… on the enumerative and algebraic properties of matroids and hyperplane arrangements. In particular, a central object of study is the Tutte polynomial, which stores much of the enumerative information of these objects. The first project is the study of the Tutte polynomial of an arrangement and, …
-
Algebraic geometry for tensor networks, matrix multiplication, and flag matroids
… we apply algebro-geometric methods to study matroids and flag matroids. We review a geometric interpretation of the Tutte polynomial in terms of the equivariant K-theory of the Grassmannian. By generalizing Grassmannians to partial flag varieties, we obtain a new invariant of flag matroids: …
-
Lattice Subdivisions and Tropical Oriented Matroids, Featuring Products of Simplices
Subdivisions of products of simplices, and their applications, appear across mathematics. In this thesis, they are the tie between two branches of my research: polytopal lattice subdivisions and tropical oriented matroid theory. The first chapter describes desirable combinatorial properties of …
-
A lattice structure on code metrics and beyond f-vectors of matroids
Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2025-12-01
-
Maximum-Sized Matroids with no Minors Isomorphic to U2,5, F7, F7¯, OR P7
Let M be the class of simple matroids which do not contain the 5-point line U2,5 , the Fano plane F7 , the non-Fano plane F7- , or the matroid P7 , as minors. Let h(n) be the maximum number of points in a rank-n matroid in M. We show that h(2)=4, h(3)=7, and h(n)=n(n+1)/2 for n>3, and we also find …
-
Selected Problems on Matroid Minors
This dissertation begins with an introduction to matroids and graphs. In the first chapter, we develop matroid and graph theory definitions and preliminary results sufficient to discuss the problems presented in the later chapters. These topics include duality, connectivity, matroid minors, and …
-
The Characterization Of Graphs With Small Bicycle Spectrum
Matroids designs are defined to be matroids in which the hyperplanes all have the same size. The dual of a matroid design is a matroid with all circuits of the same size, called a dual matroid design. The connected bicircular dual matroid designs have been characterized previously. In addition, …
-
Ramsey Theory Using Matroid Minors
… a Ramsey Theory question for graphs and regular matroids. Specifically, how many elements N are required in a 3-connected graphic or regular matroid to force the existence of certain specified minors in that matroid? This question cannot be answered for an arbitrary collection of specified …
-
Tractability through approximation : a study of two discrete optimization problems
… the solution produced by such an algorithm for matroids. We then define a continuous relaxation of the original problem and show that some of the derived bounds apply with respect to the relaxed problem. We also report on a new bound for independence systems. These bounds extend, and in some …
-
Generating secret in a network
… results. A framework is also developed to view matroids as graphs, allowing certain theory on graphs to generalize to matroids. In order to study cooperation schemes in a network, a general channel model with multiple inputs is formulated. Single-letter secrecy capacity upper bounds are derived …
-
The topology of Baues complexes and flip graphs
… of extension spaces of realizable oriented matroids. This thesis covers the main construction which is common to these proofs, but defers the details specific to each problem to other papers.
Page 1 of 2