Results 41 to 50 of about 4,266 (227)
Invariants of vector configurations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We investigate the Zariski closure of the projective equivalence class of a matrix. New results are presented regarding the matrices in this variety and their matroids, and we give equations for the variety.
Andrew Berget, Alex Fink
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A characterization of the base-matroids of a graphic matroid
Contributions to Discrete Mathematics, 2010 Let M=(E,F) be a matroid on a set E and B one of its bases. A closed set θ⊆E is saturated with respect to B when |θ∩B|≤r(θ), where r(θ) is the rank of θ. The collection of subsets I of E such that |I∩θ|≤r(θ) for every closed saturated set θ turns out to be the family of independent sets of a new matroid on E, called base-matroid and denoted by MB.
MAFFIOLI, FRANCESCO, ZAGAGLIA, NORMA
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A chain theorem for internally 4-connected binary matroids
, 2011 This is the post-print version of the Article - Copyright @ 2011 ElsevierLet M be a matroid. When M is 3-connected, Tutte’s Wheels-and-Whirls Theorem proves that M has a 3-connected proper minor N with |E(M) − E(N)| = 1 unless M is a wheel or a whirl ...
Chun, Carolyn +8 more
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Internally 4-connected binary matroids with cyclically sequential orderings
, 2009 We characterize all internally 4-connected binary matroids M with the property that the ground set of M can be ordered (e0,…,en−1) in such a way that {ei,…,ei+t} is 4-separating for all 0≤i,t≤n−1 (all subscripts are read modulo n).
Chun, Carolyn +11 more
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, 2003 Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry. This largely self-contained work provides an intuitive and interdisciplinary treatment of Coxeter matroids, a new and beautiful generalization of ...
Borovik, Alexandre V +7 more
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Characterizing matroids whose bases form graphic delta-matroids
, 2021 We introduce delta-graphic matroids, which are matroids whose bases form graphic delta-matroids. The class of delta-graphic matroids contains graphic matroids as well as cographic matroids and is a proper subclass of the class of regular matroids.
Oum, Sang-il +3 more
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Applications of Matrices to a Matroidal Structure of Rough Sets
Journal of Applied Mathematics, 2013 Rough sets provide an efficient tool for dealing with the vagueness and granularity in information systems. They are widely used in attribute reduction in data mining. There are many optimization issues in attribute reduction.
Jingqian Wang, William Zhu
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Combinatorics of Positroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 Recently Postnikov gave a combinatorial description of the cells in a totally-nonnegative Grassmannian. These cells correspond to a special class of matroids called positroids.
Suho Oh
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Edge‐Length Preserving Embeddings of Graphs Between Normed Spaces
Journal of Graph Theory, Volume 112, Issue 4, Page 491-506, August 2026.ABSTRACT The concept of graph embeddability, initially formalized by Belk and Connelly and later expanded by Sitharam and Willoughby, extends the question of embedding finite metric spaces into a given normed space. A finite simple graph G = ( V , E ) is said to be ( X , Y )‐embeddable if any set of induced edge lengths from an embedding of G into a ...
Sean Dewar +3 more
wiley +1 more source
Advances in Applied MathematicsWe show that an adjoint of a loopless matroid is connected if and only if it itself is connected. Our first goal is to study the adjoint of modular matroids. We prove that a modular matroid has only one adjoint (up to isomorphism) which can be given by its opposite lattice, and proceed to present some alternative characterizations of modular matroids ...
Houshan Fu, Chunming Tang, Suijie Wang
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