Results 21 to 30 of about 759 (82)
Disjoint cocircuits in matroids with large rank
Journal of Combinatorial Theory, Series B, 2003 To gain insight into minor-closed classes of GF\((q)\)-representable matroids that omit a given characteristic, the authors prove the following theorem: For any positive integers \(n, k\), and \(q\), there exists an integer \(R\) such that, if \(M\) is a matroid with no \(M(K_n)\)- or \(U_{2, q+2}\)-minor, then either \(M\) has a collection of \(k ...
Geelen, J.F. +2 more
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Non-separating cocircuits in matroids
Electronic Notes in Discrete Mathematics, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lemos, Manoel, Melo, T.R.B.
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Sign variation, the Grassmannian, and total positivity [PDF]
, 2015 The totally nonnegative Grassmannian is the set of k-dimensional subspaces V of R^n whose nonzero Pluecker coordinates all have the same sign. Gantmakher and Krein (1950) and Schoenberg and Whitney (1951) independently showed that V is totally ...
Karp, Steven N.
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Oriented Matroids -- Combinatorial Structures Underlying Loop Quantum Gravity [PDF]
, 2010 We analyze combinatorial structures which play a central role in determining spectral properties of the volume operator in loop quantum gravity (LQG).
Arnowitt R +48 more
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European Journal of Combinatorics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Rainbow and monochromatic circuits and cocircuits in binary matroids
Discrete Mathematics, 2022 Given a matroid with a coloring of its ground set, this coloring is called rainbow circuit-free provided any circuit contains two elements of the same color. The authors concentrate on binary matroids in the paper under review. Motivated by previous work [\textit{K. Bérczi} et al., SIAM J. Discrete Math. 35, No.
Kristóf Bérczi, Tamás Schwarcz
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Cubic Time Recognition of Cocircuit Graphs of Uniform Oriented Matroids [PDF]
, 2010 We present an algorithm which takes a graph as input and decides in cubic time if the graph is the cocircuit graph of a uniform oriented matroid. In the affirmative case the algorithm returns the set of signed cocircuits of the oriented matroid.
Felsner, Stefan +4 more
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The Tutte Polynomial of a Morphism of Matroids 5. Derivatives as Generating Functions of Tutte Activities [PDF]
, 2012 We show that in an ordered matroid the partial derivative \partial^{p+q}t/\partialx^p\partialyq of the Tutte polynomial is p!q! times the generating function of activities of subsets with corank p and nullity q.
Vergnas, Michel Las
core
A notion of minor-based matroid connectivity
, 2018 For a matroid $N$, a matroid $M$ is $N$-connected if every two elements of $M$ are in an $N$-minor together. Thus a matroid is connected if and only if it is $U_{1,2}$-connected.
Gershkoff, Zachary, Oxley, James
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Fan-extensions in fragile matroids [PDF]
, 2015 If S is a set of matroids, then the matroid M is S-fragile if, for every element e in E(M), either M\e or M/e has no minor isomorphic to a member of S. Excluded-minor characterizations often depend, implicitly or explicitly, on understanding classes of ...
Chun, Carolyn +3 more
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