Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Pendavingh, R."'
Autor:
Keijsper, J. C. M., Pendavingh, R. A.
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. We also present a more general method which can handle more diverse qu
Externí odkaz:
http://arxiv.org/abs/1308.5206
Autor:
Pendavingh, R. A., van der Pol, J. G.
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 the complexity of a matroid, and present bounds on the number of matroi
Externí odkaz:
http://arxiv.org/abs/1302.1315
We show how a direct application of Shearers' Lemma gives an almost optimum bound on the number of matroids on $n$ elements.
Comment: Short note, 4 pages
Comment: Short note, 4 pages
Externí odkaz:
http://arxiv.org/abs/1210.6581
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 $\log \log m_n$ is at least $n-3/2\log n-1$. On the other hand, Piff (1973) showed that $
Externí odkaz:
http://arxiv.org/abs/1206.6270
Autor:
Pendavingh, R. A., van Zwam, S. H. M.
Publikováno v:
Adv. in Appl. Math. 50 (2013), no. 1, 228-242
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, using chain groups. We show how such representations behave under duality
Externí odkaz:
http://arxiv.org/abs/1106.3088
Autor:
Pendavingh, R. A.
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 circuits. No system of rank axioms is given. We give an easy example showi
Externí odkaz:
http://arxiv.org/abs/1004.0154
Autor:
Pendavingh, R. A., van Zwam, S. H. M.
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 inequivalent representations. The proofs of some results on these partial fie
Externí odkaz:
http://arxiv.org/abs/1003.1640
Autor:
Pendavingh, R. A., van Zwam, S. H. M.
Publikováno v:
Journal of Combinatorial Theory, Series B, vol. 100, Issue 6, pp. 510-545, 2010
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-representation matrix A of M has a submatrix B, A is a scaled P'-matrix. We show
Externí odkaz:
http://arxiv.org/abs/0806.4487
Autor:
Pendavingh, R. A., van Zwam, S. H. M.
Publikováno v:
Journal of Combinatorial Theory, Series B, vol. 100, Issue 1, pp. 36-67, 2010
There exist several theorems which state that when a matroid is representable over distinct fields F_1,...,F_k, it is also representable over other fields. We prove a theorem, the Lift Theorem, that implies many of these results. First, parts of Whit
Externí odkaz:
http://arxiv.org/abs/0804.3263
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