Results 61 to 70 of about 22,632 (241)
Excluded minors for the class of split matroids [PDF]
, 2018 The class of split matroids arises by putting conditions on the system of split hyperplanes of the matroid base polytope. It can alternatively be defined in terms of structural properties of the matroid.
Cameron, Amanda, Mayhew, Dillon
core +3 more sources
Defining the q-analogue of a matroid [PDF]
Electronic Journal of Combinatorics, 2016 This paper defines the $q$-analogue of a matroid and establishes several properties like duality, restriction and contraction. We discuss possible ways to define a $q$-matroid, and why they are (not) cryptomorphic.
Relinde Jurrius, R. Pellikaan
semanticscholar +1 more source
The Chip Firing Game and Matroid Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper we construct from a cographic matroid M, a pure multicomplex whose degree sequence is the h―vector of the the matroid complex of M. This result provesa conjecture of Richard Stanley [Sta96] in the particular case of cographic matroids.
Criel Merino
doaj +1 more source
Valuations for matroid polytope subdivisions
, 2008 We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.Comment: 19 pages.
Ardila, Federico +2 more
core +2 more sources
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
The equivariant Kazhdan-Lusztig polynomial of a matroid [PDF]
Journal of Combinatorial Theory, 2016 We define the equivariant Kazhdan-Lusztig polynomial of a matroid equipped with a group of symmetries, generalizing the nonequivariant case. We compute this invariant for arbitrary uniform matroids and for braid matroids of small rank.
Katie R. Gedeon +2 more
semanticscholar +1 more source
On Density-Critical Matroids [PDF]
, 2019 For a matroid $M$ having $m$ rank-one flats, the density $d(M)$ is $\tfrac{m}{r(M)}$ unless $m = 0$, in which case $d(M)= 0$. A matroid is density-critical if all of its proper minors of non-zero rank have lower density.
Campbell, Rutger +3 more
core +3 more sources
A Miyaoka–Yau inequality for hyperplane arrangements in CPn$\mathbb {CP}^n$
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract Let H$\mathcal {H}$ be a hyperplane arrangement in CPn$\mathbb {CP}^n$. We define a quadratic form Q$Q$ on RH$\mathbb {R}^{\mathcal {H}}$ that is entirely determined by the intersection poset of H$\mathcal {H}$. Using the Bogomolov–Gieseker inequality for parabolic bundles, we show that if a∈RH$\mathbf {a}\in \mathbb {R}^{\mathcal {H}}$ is ...
Martin de Borbon, Dmitri Panov
wiley +1 more source
Osculating geometry and higher‐order distance Loci
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first‐order tangency. We focus on the data locus of points possessing at least one critical point of the distance function ...
Sandra Di Rocco +2 more
wiley +1 more source
A tropical approach to rigidity: Counting realisations of frameworks
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract A realisation of a graph in the plane as a bar‐joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these finitely many realisations can be seen as a solution to a system of quadratic equations prescribing the distances between pairs of points.
Oliver Clarke +6 more
wiley +1 more source