Results 41 to 50 of about 759 (82)
Positively oriented matroids are realizable [PDF]
, 2013 We prove da Silva's 1987 conjecture that any positively oriented matroid is a positroid; that is, it can be realized by a set of vectors in a real vector space.
Ardila, Federico +2 more
core
Infinitesimal index: cohomology computations
, 2011 In this note several computations of equivariant cohomology groups are performed. For the compactly supported equivariant cohomology, the notion of infinitesimal index developed in arXiv:1003.3525, allows to describe these groups in terms of certain ...
De Concini, Corrado +2 more
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Non-separating cocircuits in binary matroids
Linear Algebra and its Applications, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Signed-graphic matroids with all-graphic cocircuits
Discrete Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Papalamprou, Konstantinos +1 more
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Spanning cycles in regular matroids without small cocircuits
European Journal of Combinatorics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Ping +3 more
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The Circuit-Cocircuit Intersection Conjecture for Intersection Size $\le7$
, 2023 A circuit-cocircuit intersection, or a CCI for short, of a matroid is the intersection of a circuit and a cocircuit. Oxley conjectured (1992) that a matroid with a CCI of size $k\ge4$ has a CCI of size $k-2$. We show that the conjecture holds for $k\le7$.
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On elements in small cocircuits in minimally k-connected graphs and matroids
Discrete Mathematics, 2002 The authors prove that in a minimally \(k\)-connected graph \(G\) with \(n\) vertices and \(e\) edges, the number of edges that are incident to a vertex of degree \(k\) is at least \(\lfloor\frac{e+7}{2}\rfloor\), if \(k=2\) and \(e\geq 6\), \(\lceil\frac{2e+12}{3}\rceil\), if \(k=3\) and \(e\geq 14\), and \(\frac{(k-1)e+3k+1}{k}\), if \(k\geq 3\) and \
Reid, Talmage James, Wu, Haidong
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A module-theoretic approach to matroids
, 2019 Speyer recognized that matroids encode the same data as a special class of tropical linear spaces and Shaw interpreted tropically certain basic matroid constructions; additionally, Frenk developed the perspective of tropical linear spaces as modules over
Crowley, Colin +2 more
core
Une relation de séparation entre cocircuits d'un matroide
Journal of Combinatorial Theory, Series B, 1974 AbstractLet S1′S2′S3′ be 3 distinct cocircuits of a matroid M on a set E. We say that S1′ does not separate S2′ and S3′ when S2′\S1′ and S3′\S1′ are included in one single and the same component of the submatroid M × (E\S1′). Our main result is: A matroid is graphic if and only if from any 3 cocircuits having a non-empty intersection there is at least ...
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The Circuit-Cocircuit Intersection Conjecture for Intersection Size $k\le6$
, 2021 Oxley conjectured (1992) that if a matroid has a circuit-cocircuit intersection of size $k\ge4$, it has a circuit-cocircuit intersection of size $k-2$. We show that this conjecture holds for $k\le6$.
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