38 citations · 128 across the 24 of their papers we have counts for
25 papers · 1 filter
Counting q-Matroids
Benjamin Jany, Relinde Jurrius, Rudi Pendavingh
-Matroids, a -analogue of classical matroids have attracted a lot of attention over the last decade, yet their enumeration remains largely unexplored. In this paper, we study…
Bounds on the number of cells and the dimension of the Dressian
Rudi Pendavingh
The {\em Dressian} of a matroid is the set of all valuations of . This Dressian is the support of a polyhedral complex whose open cells correspond 1-1 with…
A linear bound for the Colin de Verdière parameter for graphs embedded on surfaces
Camille Lanuel, Francis Lazarus, Rudi Pendavingh
We provide a combinatorial and self-contained proof that for all graphs embedded on a surface , the Colin de Verdière parameter is upper bounded by .
The amoeba dimension of a linear space
Jan Draisma, Sarah Eggleston, Rudi Pendavingh +2
Given a complex vector subspace of , the dimension of the amoeba of depends only on the matroid that defines on the ground set $\{1,…
Computing excluded minors for classes of matroids representable over partial fields
Nick Brettell, Rudi Pendavingh
We describe an implementation of a computer search for the "small" excluded minors for a class of matroids representable over a partial field. Using these techniques, we enumerate…
How to Design a Stable Serial Knockout Competition
Frits Spieksma, Rudi Pendavingh, Roel Lambers
We investigate a new tournament format that consists of a series of individual knockout tournaments; we call this new format a Serial Knockout Competition (SKC). This format has re…
Von Staudt Constructions for Skew-Linear and Multilinear Matroids
Lukas Kühne, Rudi Pendavingh, Geva Yashfe
This paper compares skew-linear and multilinear matroid representations. These are matroids that are representable over division rings and (roughly speaking) invertible matrices, r…
Perfect matroids over hyperfields
Nathan Bowler, Rudi Pendavingh
We investigate valuated matroids with an additional algebraic structure on their residue matroids. We encode the structure in terms of representability over stringent hyperfields.…
Field extensions, Derivations, and Matroids over Skew Hyperfields
Rudi Pendavingh
We show that a field extension in positive characteristic and elements for gives rise to a matroid on ground set with coefficients…
Algebraic matroids and Frobenius flocks
Guus Bollen, Jan Draisma, Rudi Pendavingh
We show that each algebraic representation of a matroid in positive characteristic determines a matroid valuation of , which we have named the {\em Lindström valuation}. If…
Asymptotics of Symmetry in Matroids
Rudi Pendavingh, Jorn van der Pol
We prove that asymptotically almost all matroids have a trivial automorphism group, or an automorphism group generated by a single transposition. Additionally, we show that asympto…
On the number of bases of almost all matroids
Rudi Pendavingh, Jorn van der Pol
For a matroid of rank on elements, let denote the fraction of bases of among the subsets of the ground set with cardinality . We show that $$Ω(1/n)\leq 1-…
Enumerating matroids of fixed rank
Rudi Pendavingh, Jorn van der Pol
It has been conjectured that asymptotically almost all matroids are sparse paving, i.e. that , where denotes the number of matroids on a fixed groundset of s…
On the number of matroids compared to the number of sparse paving matroids
Rudi Pendavingh, Jorn van der Pol
It has been conjectured that sparse paving matroids will eventually predominate in any asymptotic enumeration of matroids, i.e. that , where…
Reconstructing a phylogenetic level-1 network from quartets
J. C. M. Keijsper, R. A. Pendavingh
We describe a method that will reconstruct an unrooted binary phylogenetic level-1 network on n taxa from the set of all quartets containing a certain fixed taxon, in O(n^3) time.…
Counting matroids in minor-closed classes
R. A. Pendavingh, J. G. van der Pol
A flat cover is a collection of flats identifying the non-bases of a matroid. We introduce the notion of cover complexity, the minimal size of such a flat cover, as a measure for t…
An entropy argument for counting matroids
N. Bansal, R. A. Pendavingh, J. G. van der Pol
We show how a direct application of Shearers' Lemma gives an almost optimum bound on the number of matroids on elements.
On the number of matroids
N. Bansal, R. A. Pendavingh, J. G. van der Pol
We consider the problem of determining , the number of matroids on elements. The best known lower bound on is due to Knuth (1974) who showed that is…
On the evaluation at (-i,i) of the Tutte polynomial of a binary matroid
Rudi Pendavingh
Vertigan has shown that if is a binary matroid, then , the modulus of the Tutte polynomial of as evaluated in , can be expressed in terms of the bicyc…
Representing some non-representable matroids
R. A. Pendavingh, S. H. M. van Zwam
We extend the notion of representation of a matroid to algebraic structures that we call skew partial fields. Our definition of such representations extends Tutte's definition, usi…
Relative rank axioms for infinite matroids
R. A. Pendavingh
In a recent paper, Bruhn, Diestel, Kriesell and Wollan (arXiv:1003.3919) present four systems of axioms for infinite matroids, in terms of independent sets, bases, closure and circ…
The Hydra-k partial fields
R. A. Pendavingh, S. H. M. van Zwam
In the paper "Confinement of matroid representations to subsets of partial fields" (arXiv:0806.4487) we introduced the Hydra-k partial fields to study quinary matroids with inequiv…
Axioms for infinite matroids
Henning Bruhn, Reinhard Diestel, Matthias Kriesell +2
We give axiomatic foundations for non-finitary infinite matroids with duality, in terms of independent sets, bases, circuits, closure and rank. This completes the solution to a pro…
Confinement of matroid representations to subsets of partial fields
R. A. Pendavingh, S. H. M. van Zwam
Let M be a matroid representable over a (partial) field P and B a matrix representable over a sub-partial field P' of P. We say that B confines M to P' if, whenever a P-representat…