Results 11 to 20 of about 14,016 (208)
Approximate‐Guided Representation Learning in Vision Transformer
CAAI Transactions on Intelligence TechnologyIn recent years, the transformer model has demonstrated excellent performance in computer vision (CV) applications. The key lies in its guided representation attention mechanism, which uses dot‐product to depict complex feature relationships, and ...
Kaili Wang +4 more
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Regular Matroids with Graphic Cocircuits [PDF]
Electronic Proceedings in Theoretical Computer Science, 2009 We introduce the notion of graphic cocircuits and show that a large class of regular matroids with graphic cocircuits belongs to the class of signed-graphic matroids.
Konstantinos Papalamprou +1 more
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SIAM Journal on Discrete Mathematics, 2023 For all positive integers $s$ and $t$ exceeding one, a matroid $M$ on $n$ elements is {\em nearly $(s, t)$-cyclic} if there is a cyclic ordering $σ$ of its ground set such that every $s-1$ consecutive elements of $σ$ are contained in an $s$-element circuit and every $t-1$ consecutive elements of $σ$ are contained in a $t$-element cocircuit. In the case
Nick Brettell +2 more
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Proceedings of the American Mathematical Society, 1971 There are several known results concerning how matroids can be induced from given matroids by a bipartite graph and the properties that are inherited in this way. The purpose of this note is to extend some of these results to the situation where the bipartite graph is replaced by an arbitrary directed graph.
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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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Kazhdan-Lusztig polynomials of fan matroids, wheel matroids, and whirl matroids
Journal of Combinatorial Theory, Series A, 2022 60 pages, 15 ...
Lu, Linyuan +2 more
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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 ...
Bonin, Joseph E., Schmitt, William R.
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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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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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Journal of Algebraic Combinatorics, 1998 A Coxeter matroid, also called WP-matroid, is a subset \(M\) of the set of cosets \(W/P\) of a Coxeter group \(W\) modulo a parabolic subgroup \(P\) such that \(M\) satisfies a certain maximality condition. More precisely, for each \(w\in W\) there is an element \(x\in M\) such that for all \(y\in M\) the element \(w^{-1}y\) precedes or equals \(w^{-1 ...
Borovik, Alexandre V. +2 more
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