Results 21 to 30 of about 22,632 (241)
On n-connected minors of the es-splitting binary matroids
Electronic Journal of Graph Theory and Applications, 2021 The es-splitting operation on an n-connected binary matroid may not yield an n-connected matroid for (n ≥ 3). In this paper, we show that given an n-connected binary matroid M of rank r, the resulting es-splitting binary matroid has an n-connected minor ...
Prashant Pralhad Malavadkar +2 more
doaj +1 more source
Faster Matroid Intersection [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2019 In this paper we consider the classic matroid intersection problem: given two matroids M_1=(V, I_1) and M_2=(V, I_2) defined over a common ground set V, compute a set S∊I_1 ∩ I_2 of largest possible cardinality, denoted by r.
Deeparnab Chakrabarty +4 more
semanticscholar +1 more source
A new matroid constructed by the rank function of a matroid
AKCE International Journal of Graphs and Combinatorics, 2020 In this article, we construct a submodular function using the rank function of a matroid and study induced matroid with constructed polymatroid, then we relate some properties of connectivity of new matroid with the main matroid.
Moein Pourbaba +2 more
doaj +1 more source
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
openaire +3 more sources
Linear Algebraic Relations among Cardinalities of Sets of Matroid Functions
Mathematics, 2023 We introduce a unifying approach for invariants of finite matroids that count mappings to a finite set. The aim of this paper is to show that if the cardinalities of mappings with fixed values on a restricted set satisfy contraction–deletion rules, then ...
Martin Kochol
doaj +1 more source
From weakly separated collections to matroid subdivisions [PDF]
Combinatorial Theory, 2019 We study arrangements of slightly skewed tropical hyperplanes, called blades by A. Ocneanu, on the vertices of a hypersimplex $\Delta_{k,n}$, and we investigate the resulting induced polytopal subdivisions.
Nick Early
semanticscholar +1 more source
Generalized permutohedra, h-vectors of cotransversal matroids and pure O-sequences (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Stanley has conjectured that the h-vector of a matroid complex is a pure O-sequence. We will prove this for cotransversal matroids by using generalized permutohedra. We construct a bijection between lattice points inside a $r$-dimensional convex polytope
Suho Oh
doaj +1 more source
Matroids related to groups and semigroups
Researches in Mathematics, 2023 Matroid is defined as a pair $(X,\mathcal{I})$, where $X$ is a nonempty finite set, and $\mathcal{I}$ is a nonempty set of subsets of $X$ that satisfies the Hereditary Axiom and the Augmentation Axiom.
D.I. Bezushchak
doaj +1 more source
An optimal approximation for submodular maximization under a matroid constraint in the adaptive complexity model [PDF]
Symposium on the Theory of Computing, 2018 In this paper we study submodular maximization under a matroid constraint in the adaptive complexity model. This model was recently introduced in the context of submodular optimization to quantify the information theoretic complexity of black-box ...
Eric Balkanski +2 more
semanticscholar +1 more source
Relations between M\"obius and coboundary polynomial [PDF]
, 2012 It is known that, in general, the coboundary polynomial and the M\"obius polynomial of a matroid do not determine each other. Less is known about more specific cases.
A. Faldum +15 more
core +3 more sources