J. G. van der Pol

activity

20122022

collaborators

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10 papers · 1 filter

math.CO2022

Random GF(q)-representable matroids are not (b,c)-decomposable

Jorn van der Pol

We show that a random subset of the rank- $n$ projective geometry $PG (n - 1, q)$ is, with high probability, not $(b, c)$ -decomposable: if $k$ is its colouring number, it does not…

math.CO2021

Tuza's conjecture for binary geometries

Kazuhiro Nomoto, Jorn van der Pol

Tuza (A conjecture, in Proceedings of the Colloquia Mathematica Societatis Janos Bolyai, 1981) conjectured that $τ (G) \leq 2 ν (G)$ for all graphs $G$ , where $τ (G)$ is the minimum siz…

math.CO2021

Almost every matroid has an $M (K_{4})$ - or a $W^{3}$ -minor

Jorn van der Pol

We show that almost every matroid contains the rank-3 whirl $W^{3}$ or the complete-graphic matroid $M (K_{4})$ as a minor.

math.CO2021

Enumeration of extensions of the cycle matroid of a complete graph

Peter Nelson, Shayla Redlin, Jorn van der Pol

We prove that the number of single element extensions of $M (K_{n + 1})$ is $2^{(n /2 n) (1 + o (1))}$ . This is done using a characterization of extensions as "linear subclasses".

math.CO2018

The number of partial Steiner systems and $d$ -partitions

Remco van der Hofstad, Rudi Pendavingh, Jorn van der Pol

We prove asymptotic upper bounds on the number of $d$ -partitions (paving matroids of fixed rank) and partial Steiner systems (sparse paving matroids of fixed rank), using a mixture…

math.CO2016

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…

math.CO2016

On the number of bases of almost all matroids

Rudi Pendavingh, Jorn van der Pol

For a matroid $M$ of rank $r$ on $n$ elements, let $b (M)$ denote the fraction of bases of $M$ among the subsets of the ground set with cardinality $r$ . We show that $$Ω(1/n)\leq 1-…

math.CO2016

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 $s (n) \sim m (n)$ , where $m (n)$ denotes the number of matroids on a fixed groundset of s…

math.CO2014

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 $lim_{n \to \infty} s_{n} / m_{n} = 1$ , where…

math.CO2012

On the number of matroids

N. Bansal, R. A. Pendavingh, J. G. van der Pol

We consider the problem of determining $m_{n}$ , the number of matroids on $n$ elements. The best known lower bound on $m_{n}$ is due to Knuth (1974) who showed that $lo g lo g m_{n}$ is…

Random GF(q)-representable matroids are not (b,c)-decomposable

Tuza's conjecture for binary geometries

Almost every matroid has an M(K4​)- or a W3-minor

Enumeration of extensions of the cycle matroid of a complete graph

The number of partial Steiner systems and d-partitions

Asymptotics of Symmetry in Matroids

On the number of bases of almost all matroids

Enumerating matroids of fixed rank

On the number of matroids compared to the number of sparse paving matroids

On the number of matroids

Almost every matroid has an $M (K_{4})$ - or a $W^{3}$ -minor

The number of partial Steiner systems and $d$ -partitions