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Now showing items 11-17 of 17

#### An upgraded wheels-and-whirls theorem for 3-connected matroids

(University of Canterbury. Dept. of Mathematics and Statistics, 2009)

Let M be a 3-connected matroid that is not a wheel or a
whirl. In this paper, we prove that M has an element e such that M\e
or M/e is 3-connected and has no 3-separation that is not equivalent to
one induced by M.

#### The structure of equivalent 3-separations in a 3-connected matroid

(University of Canterbury, 2004)

Let M be a matroid. When M is 2-connected, Cunningham and Edmonds gave a tree decomposition of M that displays all of its 2-separations. This result was extended by Oxley, Semple, and Whittle, who showed that, when M is ...

#### Fork-decompositions of matroids

(University of Canterbury, 2002)

One of the central problems in matroid theory is Rota's conjecture
that, for all prime powers q, the class of GF(q)-representable matroids has a
finite set of excluded minors. This conjecture has been settled for q ≤ 4 ...

#### The structure of the 3-separations of 3-connected matroids II

(University of Canterbury. Dept. of Mathematics and Statistics, 2005)

The authors showed in an earlier paper that there is a tree that displays, up to a natural equivalence, all non-trivial 3-separations of a 3-connected matroid. The purpose of this paper is to show that if certain natural ...

#### Adaptive sampling: my journey that began in the Department of Mathematics and Statistics, Otago University

(University of Canterbury. Mathematics and Statistics, 2011)

#### Rapid evaluation of least squares and minimum evolution criteria on phylogenetic trees

(University of Canterbury. Dept. of Mathematics, 1997)

We present fast new algorithms for evaluating trees with respect to least squares and minimum evolution (ME), the most commonly used criteria for
inferring phylogenetic trees from distance data. These include: an ...

#### The seventeen wallpaper groups

(University of Canterbury. Mathematics and Statistics, 2007)

Wallpaper patterns are categorised into lattices. A case-by-case analysis of each group of orthogonal transformations which preserve a lattice is used to develop the seventeen wallpaper groups. All the elements of each ...