## Search

Now showing items 1-10 of 17

#### In search of 4 - (12,6,4) designs. Part I

(University of Canterbury, 1993)

As a first step towards finding all 4-(12, 6, 4) designs which are not 5-(12, 6, 1)
designs, it is shown that if such a design has a pair of blocks with five points in common,
then there is a unique way of assigning the ...

#### Wild triangles in 3-connected matroids

(University of Canterbury, 2006)

Tutte's Triangle Lemma proves that if {a, b, c} is a triangle in a 3-connected matroid and neither M\a nor M\b is 3-connected, then M has a triad that contains a and exactly one of b and c. Hence {a, b, c} is contained in ...

#### The structure of 3-connected matroids of path width three

(University of Canterbury, 2005)

A 3-connected matroid M is sequential or has path width 3 if its ground set E(M) has a sequential ordering, that is, an ordering (e₁, e₂, ... , ek) such that ({e₁,e₂, .. ,,ek}, {ek+₁,ek+₂, .. ,,en}) is a 3-separation for ...

#### Four characters suffice to convexly define a phylogenetic tree

(University of Canterbury, 2002)

It was recently shown that just five characters (functions on a finite set X) suffice to convexly define a trivalent tree with leaf set X. Here we show that four characters suffice which, since three characters is not ...

#### A chain theorem for matroids

(University of Canterbury, 2006)

Tutte's Wheels-and-Whirls Theorem proves that if M is a 3-connected matroid other than a wheel or a whirl, then M has a 3-connected minor N such that |E(M)| - |E(N)| = 1. Geelen and Whittle extended this theorem by showing ...

#### Infinite antichains of matroids with characteristic set {p}

(University of Canterbury, 1999)

For each prime p, we construct an infinite antichain of matroids in
which each matroid has characteristic set {p}. For p=2, each of the matroids
in our antichain is an excluded minor for the class of matroids representable ...

#### Negative correlation in graphs and matroids

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

The following two conjectures arose in the work of Grimmett
and Winkler, and Pemantle: the uniformly random forest F and
the uniformly random connected subgraph C of a finite graph G have
the edge-negative-association ...

#### Shortest path algorithms for nearly acyclic directed graphs

(University of Canterbury. Computer Science and Software Engineering, 1997)

Abuaiadh and Kingston gave an efficient algorithm for the single source shortest path problem for a nearly acyclic graph with O(m+n log t) computing time, where m and n are the numbers of edges and vertices of the given ...

#### Determinantal identities for modular Schur symmetric functions

(University of Canterbury. Dept. of Mathematics, 1995)

Modular symmetric functions are a new class of symmetric functions which depend both on a partition ⋋ and an integer modulus
p > 2. For p prime, these functions have representation theoretic
significance as the irreducible ...

#### Some remarks on a family of T-designs

(University of Canterbury. Dept. of Mathematics, 1981)

In a (2m-2) - (4m-1, 2m, m) design there can be no repeated blocks, every two blocks have at least two points
in common, and no two blocks can have more than 2m-2 points
in common.