Results 41 to 50 of about 4,009 (153)
On Serial Symmetric Exchanges of Matroid Bases [PDF]
Journal of Graph Theory, 2012 AbstractWe study some properties of a serial (i.e., one‐by‐one) symmetric exchange of elements of two disjoint bases of a matroid. We show that any two elements of one base have a serial symmetric exchange with some two elements of the other base. As a result, we obtain that any two disjoint bases in a matroid of rank 4 have a full serial symmetric ...
Kotlar, Daniel, Ziv, Ran
openaire +3 more sources
Toric amplitudes and universal adjoints
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract A toric amplitude is a rational function associated with a simplicial polyhedral fan. The definition is inspired by scattering amplitudes in particle physics. We prove algebraic properties of such amplitudes and study the geometry of their zero loci. These hypersurfaces play the role of Warren's adjoint via a dual volume interpretation.
Simon Telen
wiley +1 more source
On circuits and serial symmetric basis-exchange in matroids [PDF]
, 2012 The way circuits, relative to a basis, are affected as a result of exchanging a basis element, is studied. As consequences, it is shown that three consecutive symmetric exchanges exist for any two bases of a matroid, and that a full serial symmetric ...
Kotlar, Daniel
core
A simple PTAS for weighted matroid matching on strongly base orderable matroids [PDF]
Discrete Applied Mathematics, 2011 8 pages, 3 figures.
openaire +4 more sources
On higher Jacobians, Laplace equations, and Lefschetz properties
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Let A$A$ be a standard graded Artinian K$\mathbb {K}$‐algebra over a field of characteristic zero. We prove that the failure of strong Lefschetz property (SLP) for A$A$ is equivalent to the osculating defect of a certain rational variety.
Charles Almeida +2 more
wiley +1 more source
An algorithm for determining the bases of a regular matroid
Journal of Numerical Analysis and Approximation Theory, 1988 Not available.
Dănuţ Marcu
doaj +2 more sources
On the Caratheodory rank of polymatroid bases [PDF]
, 2010 In this paper we prove that the Carath\'eodory rank of the set of bases of a (poly)matroid is upper bounded by the cardinality of the ground set.Comment: 7 ...
Gijswijt, Dion, Regts, Guus
core
A Tverberg type theorem for matroids
, 2016 Let b(M) denote the maximal number of disjoint bases in a matroid M. It is shown that if M is a matroid of rank d+1, then for any continuous map f from the matroidal complex M into the d-dimensional Euclidean space there exist t \geq \sqrt{b(M)}/4 ...
A. Björner +10 more
core +1 more source
Canonical forms of oriented matroids
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Positive geometries are semialgebraic sets equipped with a canonical differential form whose residues mirror the boundary structure of the geometry. Every full‐dimensional projective polytope is a positive geometry. Motivated by the canonical forms of polytopes, we construct a canonical form for any tope of an oriented matroid inside the Orlik–
Christopher Eur, Thomas Lam
wiley +1 more source
Computing Algebraic Matroids [PDF]
, 2014 An affine variety induces the structure of an algebraic matroid on the set of coordinates of the ambient space. The matroid has two natural decorations: a circuit polynomial attached to each circuit, and the degree of the projection map to each base ...
Rosen, Zvi
core