Results 31 to 40 of about 4,266 (227)

Minor-closed classes of binary functions [PDF]

Discrete Mathematics & Theoretical Computer Science
Binary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid deletion and ...
Benjamin R. Jones
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Laminar matroids

European Journal of Combinatorics, 2017
A laminar family is a collection $\mathscr{A}$ 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 $\mathscr{A}$, let $\mathscr{I}$ be $\{I:|I\cap A| \leq c(A)\text{ for all $A\in\mathscr{A}$}\}$.
Tara Fife, James G. Oxley
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Graphic and Cographic Г-Extensions of Binary Matroids

Discussiones Mathematicae Graph Theory, 2018
Slater introduced the point-addition operation on graphs to characterize 4-connected graphs. The Г-extension operation on binary matroids is a generalization of the point-addition operation. In general, under the Г-extension operation the properties like
Borse Y.M., Mundhe Ganesh
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On matroids of branch-width three [PDF]

, 2001
For the abstract of this paper, please see the PDF ...
Whittle, G, Oxley, James, Oxley, J, Whittle, G., Hall, R., Semple, Charles, Semple, C, Oxley, J., Hall, R, Geoff Whittle, Semple, C., Charles Semple, Whittle, Geoff, Rhiannon Hall, James Oxley, Hall, Rhiannon   +15 more
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Flag Matroids: Algebra and Geometry

, 2022
Matroids are ubiquitous in modern combinatorics. As discovered by Gel’fand, Goresky, MacPherson and Serganova there is a beautiful connection between matroid theory and the geometry of Grassmannians: representable matroids correspond to torus orbits in ...
Cameron, Amanda, Dinu, Rodica, Seynnaeve, Tim, Michałek, Mateusz   +3 more
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The structure of 3-connected matroids of path width three [PDF]

, 2007
For the abstract of this paper, please see the PDF ...
Oxley, James, Oxley, J, Semple, C., Hall, Rhiannon, Hall, R., Semple, Charles, Semple, C, Oxley, J., Hall, R   +8 more
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A lattice point counting generalisation of the Tutte polynomial [PDF]

Discrete Mathematics & Theoretical Computer Science, 2020
The Tutte polynomial for matroids is not directly applicable to polymatroids. For instance, deletion- contraction properties do not hold. We construct a polynomial for polymatroids which behaves similarly to the Tutte polynomial of a matroid, and in fact
Amanda Cameron, Alex Fink
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Factorization theorems for strong maps between matroids of arbitrary cardinality

Open Mathematics, 2016
In this paper we present factorization theorems for strong maps between matroids of arbitrary cardinality. Moreover, we present a new way to prove the factorization theorem for strong maps between finite matroids.
Mao Hua
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A Note on Ultrametric Spaces, Minimum Spanning Trees and the Topological Distance Algorithm

Information, 2020
We relate the definition of an ultrametric space to the topological distance algorithm—an algorithm defined in the context of peer-to-peer network applications.
Jörg Schäfer
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Matroids on the Bases of Simple Matroids

European Journal of Combinatorics, 1981
Let M be a simple matroid (= combinatorial geometry). On the bases of M we consider two matroids S(M, F) and H(M, F), which depend on a field F. S(M, F) is the simplicial matroid with coefficients in F on the bases of M considered as simplices. H(M, F) has been studied by Björner in [1].
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