Results 11 to 20 of about 507 (44)
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 2, Page 401-410, 1999., 1999 We show that for ⌊d/2⌋ ≤ k ≤ d, the relative interior of every k‐face of a d‐simplex Δd can be intersected by a 2(d − k)‐dimensional affine flat. Bezdek, Bisztriczky, and Connelly′s results [2] show that the condition k ≥ ⌊d/2⌋ above cannot be dropped and hence raise the question of determining, for all 0 ≤ k, j < d, an upper bound on the function c(j,
Nagabhushana Prabhu
wiley +1 more source
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
doaj +1 more source
The Arithmetic Tutte polynomial of two matrices associated to Trees
Special Matrices, 2018 Arithmetic matroids arising from a list A of integral vectors in Zn are of recent interest and the arithmetic Tutte polynomial MA(x, y) of A is a fundamental invariant with deep connections to several areas. In this work, we consider two lists of vectors
Bapat R. B. +1 more
doaj +1 more source
On Rota's Conjecture and nested separations in matroids [PDF]
, 2015 We prove that for each finite field $\mathbb F$ and integer $k\in \mathbb Z$ there exists $n\in \mathbb Z$ such that no excluded minor for the class of $\mathbb F$-representable matroids has $n$ nested $k$-separations.Comment: 12 pages.
Ben-David, Shalev, Geelen, Jim
core +1 more source
Noether normalizations, reductions of ideals, and matroids [PDF]
, 2010 We show that given a finitely generated standard-graded algebra of dimension $d$ over an infinite field, its graded Noether normalizations obey a certain kind of `generic exchange', allowing one to pass between any two of them in at most $d$ steps.
Brennan, Joseph P., Epstein, Neil
core +2 more sources
A greedy algorithm for interval greedoids
Open Mathematics, 2018 We show that the greedy algorithm provided in this paper works for interval greedoids with positive weights under some conditions, and also characterize an exchangeable system to be an interval greedoid with the assistance of the greedy algorithm.
Mao Hua
doaj +1 more source
Matroid toric ideals: complete intersection, minors and minimal systems of generators [PDF]
, 2015 In this paper, we investigate three problems concerning the toric ideal associated to a matroid. Firstly, we list all matroids $\mathcal M$ such that its corresponding toric ideal $I_{\mathcal M}$ is a complete intersection.
Alfonsín, Jorge Luis Ramírez +1 more
core +2 more sources
Power graphs and exchange property for resolving sets
Open Mathematics, 2019 Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton twins is given.
Abbas Ghulam +4 more
doaj +1 more source
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
doaj +1 more source
A construction of infinite sets of intertwines for pairs of matroids [PDF]
, 2010 An intertwine of a pair of matroids is a matroid such that it, but none of its proper minors, has minors that are isomorphic to each matroid in the pair.
Bonin, Joseph E.
core +1 more source