Results 21 to 30 of about 14,016 (208)
Matroids, delta-matroids and embedded graphs [PDF]
Journal of Combinatorial Theory, Series A, 2019 v2: We have split this paper into two. The later material of version 1 now appears in "On the interplay between embedded graphs and delta-matroids".
Chun, C. +3 more
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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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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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Graphic and Cographic Г-Extensions of Binary Matroids
Discussiones Mathematicae Graph Theory, 2018 Slater introduced the point-addition operation on graphs to characterize 4-connected graphs. The Г-extension operation on binary matroids is a generalization of the point-addition operation. In general, under the Г-extension operation the properties like
Borse Y.M., Mundhe Ganesh
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Minor-closed classes of binary functions [PDF]
Discrete Mathematics & Theoretical Computer ScienceBinary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid deletion and ...
Benjamin R. Jones
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The highly connected even-cycle and even-cut matroids [PDF]
, 2018 The classes of even-cycle matroids, even-cycle matroids with a blocking pair, and even-cut matroids each have hundreds of excluded minors. We show that the number of excluded minors for these classes can be drastically reduced if we consider in each ...
Grace, Kevin, van Zwam, Stefan H. M.
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European Journal of Combinatorics, 2017 A laminar family is a collection $\mathscr{A}$ of subsets of a set $E$ such that, for any two intersecting sets, one is contained in the other. For a capacity function $c$ on $\mathscr{A}$, let $\mathscr{I}$ be $\{I:|I\cap A| \leq c(A)\text{ for all $A\in\mathscr{A}$}\}$.
Fife, Tara, Oxley, James
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A lattice point counting generalisation of the Tutte polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The Tutte polynomial for matroids is not directly applicable to polymatroids. For instance, deletion- contraction properties do not hold. We construct a polynomial for polymatroids which behaves similarly to the Tutte polynomial of a matroid, and in fact
Amanda Cameron, Alex Fink
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Many 2-level polytopes from matroids [PDF]
, 2015 The family of 2-level matroids, that is, matroids whose base polytope is 2-level, has been recently studied and characterized by means of combinatorial properties.
Grande, Francesco, Rué, Juanjo
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Gorenstein graphic matroids [PDF]
Israel Journal of Mathematics, 2021 The toric variety of a matroid is projectively normal, and therefore it is Cohen-Macaulay. We provide a complete graph-theoretic classification when the toric variety of a graphic matroid is Gorenstein.
Hibi, T. +4 more
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