Results 21 to 30 of about 4,266 (227)
Tropical Oriented Matroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Tropical oriented matroids were defined by Ardila and Develin in 2007. They are a tropical analogue of classical oriented matroids in the sense that they encode the properties of the types of points in an arrangement of tropical hyperplanes – in much the
Silke Horn
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European Journal of Combinatorics, 2011 We introduce and study a natural variant of matroid amalgams. For matroids M(A) and N(B) such that M/(A-B)=N(B-A), we define a splice of M and N to be a matroid L on the union of A and B with L(B-A)=M and L/(A-B)=N. We show that splices exist for each such pair of matroids M and N; furthermore, there is a freest splice of M and N, which we call the ...
Joseph E. Bonin, William R. Schmitt
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On complete classes of valuated matroids [PDF]
TheoretiCSWe characterize a rich class of valuated matroids, called R-minor valuated matroids that includes the indicator functions of matroids, and is closed under operations such as taking minors, duality, and induction by network.
Edin Husić +3 more
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Fork-decompositions of matroids [PDF]
, 2004 For the abstract of this paper, please see the PDF ...
Whittle, G +11 more
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Graded Linearity of Stanley–Reisner Ring of Broken Circuit Complexes
Journal of Mathematics, 2022 This paper introduces two new notions of graded linear resolution and graded linear quotients, which generalize the concepts of linear resolution property and linear quotient for modules over the polynomial ring A=kx1,…,xn.
Mohammad Reza-Rahmati, Gerardo Flores
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Dendriform structures for restriction-deletion and restriction-contraction matroid Hopf algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 We endow the set of isomorphism classes of matroids with a new Hopf algebra structure, in which the coproduct is implemented via the combinatorial operations of restriction and deletion.
Nguyen Hoang-Nghia +2 more
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The Electronic Journal of Combinatorics, 2006 One way to choose a basis of a matroid at random is to choose an ordering of the ground set uniformly at random and then use the greedy algorithm to find a basis. We investigate the class of matroids having the property that this procedure yields a basis uniformly at random.
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Hierarchical Zonotopal Power Ideals [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Zonotopal algebra deals with ideals and vector spaces of polynomials that are related to several combinatorial and geometric structures defined by a finite sequence of vectors.
Matthias Lenz
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Matroid Secretary for Regular and Decomposable Matroids [PDF]
SIAM Journal on Computing, 2013 In the matroid secretary problem we are given a stream of elements and asked to choose a set of elements that maximizes the total value of the set, subject to being an independent set of a matroid given in advance. The difficulty comes from the assumption that decisions are irrevocable: if we choose to accept an element when it is presented by the ...
Michael Dinitz, Guy Kortsarz
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Matroids Over One-Dimensional Groups
, 2022 We develop the theory of matroids over one-dimensional algebraic groups, with special emphasis on positive characteristic. In particular, we compute the Lindström valuations and Frobenius flocks of such matroids. Building on work by Evans and Hrushovski,
Bollen, Guus P +2 more
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