## Search

Now showing items 1-10 of 39

#### Takenings, rames and mills : structures for the modelling of branching

(University of Canterbury. Dept. of Mathematics, 1987)

A takening is a combinatorial structure composed of points and rays. A ray is a finite sequence of at least two points, and two rays have at most one point in common, which must be the foot (initial point) of at least ...

#### A supertree method for rooted trees

(University of Canterbury. Dept. of Mathematics, 1999)

The amalgamation of leaf-labelled (phylogenetic) trees on overlapping leaf sets into one (super)tree is a central problem in several areas of
classification, particularly evolutionary biology. In this paper, we describe ...

#### On the Condition Number Distribution of Complex Wishart Matrices

(University of Canterbury. Electrical and Computer EngineeringUniversity of Canterbury. Mathematics and Statistics, 2010)

This paper investigates the distribution of the condition
number of complex Wishart matrices. Two closely related
measures are considered: the standard condition number (SCN)
and the Demmel condition number (DCN), both ...

#### Uniform diagonalisation of matrices over regular rings

(University of Canterbury. Dept. of Mathematics and Statistics, 2000)

The fundamental Separativity Problem for vorrNeumann regular rings is shown
to be equivalent to a linear algebra problem: for a field F, is there a "uniform formula"
for diagonalising a 2 x 2 matrix A over Mn(F), ...

#### A new measure of growth for countable-dimensional algebras II

(University of Canterbury. Dept. of Mathematics, 1993)

A new dimension function on countable-dimensional algebras (over a field) was introduced in the first paper I, by means of certain infinite matrix representations. Here we show that its
dimension values for finitely ...

#### A characterization for a set of partial partitions to define an X-tree

(University of Canterbury, 1999)

Trees whose vertices are partially labelled by elements of a finite
set X provide a natural way to represent partitions of subsets of X. The condition
under which a given collection of such partial partitions of X can ...

#### Rota's basis conjecture for paving matroids

(University of Canterbury, 2006)

Rota conjectured that, given n disjoint bases of a
rank-n matroid M, there are n disjoint transversals of these bases
that are all bases of M. We prove a stronger statement for the
class of paving matroids.

#### Revisiting Al-Samaw'al’s table of binomial coefficients: Greek inspiration, diagrammatic reasoning and mathematical induction

(University of Canterbury. Mathematics and Statistics, 2015)

In a famous passage from his al-Bahir, al-Samaw'al proves the identity which we would now write as (ab)^n = a^n b^n for the cases n = 3; 4. He also calculates the equivalent of the expansion of the binomial (a + b)^n for ...

#### Algorithms for the computation of approximations by algebraic functions

(University of Canterbury. Dept. of Mathematics, 1991)

The application of Pade approximation to problems in mathematical physics was introduced by Balrnr and Gammel (Baker and Gammel (1961)). Pade approximations,
the rational analogue of the Taylor polynomial approximation, ...

#### An algorithm for constructing a k-tree for a k-connected matroid

(University of Canterbury. Mathematics and Statistics, 2015)

For a k-connected matroid M, Clark and Whittle showed
there is a tree that displays, up to a natural equivalence, all non-trivial
k-separations of M. In this paper, we present an algorithm for con-
structing such a tree, ...