# Browsing by Author "Cavenagh, Nicholas J."

Now showing items 1-5 of 24

• #### Balanced diagonals in frequency squares ﻿

(Elsevier, 2018)
We say that a diagonal in an array is λ-balanced if each entry occurs λ times. Let L be a frequency square of type F (n; λ); that is, an n ✕ n array in which each entry from {1, 2, …, m=n / λ } occurs λ times per row and ...
• #### Biembeddings of cycle systems using integer Heffter arrays ﻿

(Wiley, 2020)
In this paper, we use constructions of Heffter arrays to verify the existence of face 2‐colorable embeddings of cycle decompositions of the complete graph. Specifically, for n ≡ 1 (mod 4) and k ≡3(mod 4), n k ≫ ⩾ 7 and ...
• #### Complete sets of metamorphoses: Twofold 4-cycle systems into twofold 6-cycle systems ﻿

(Elsevier, 2012)
Let (X,C) denote a twofold k-cycle system with an even number of cycles. If these k-cycles can be paired together so that: (i) each pair contains a common edge; (ii) removal of the repeated common edge from each pair leaves ...
• #### Constructing (0,1)-matrices with large minimal defining sets ﻿

(Elsevier, 2018)
If D is a partially filled-in (0, 1)-matrix with a unique completion to a (0, 1)-matrix M (with prescribed row and column sums), we say that D is a defining set for M. Let A₂ₘ,ₘbe the set of (0, 1)-matrices of dimensions ...
• #### Critical sets of 2-balanced Latin rectangles ﻿

(2016)
An (m, n, 2)-balanced Latin rectangle is an (Formula presented.) array on symbols 0 and 1 such that each symbol occurs n times in each row and m times in each column, with each cell containing either two 0’s, two 1’s or ...

Nicholas J. Cavenagh has 18 co-authors in Research Commons.

Showing up to 5 theses - most recently added to Research Commons first.

• #### Critical sets of full Latin squares ﻿

(University of Waikato, 2016)
This thesis explores the properties of critical sets of the full n-Latin square and related combinatorial structures including full designs, (m,n,2)-balanced Latin rectangles and n-Latin cubes. In Chapter 3 we study ...
• #### Star Decompositions of Bipartite Graphs ﻿

(University of Waikato, 2015)
In Chapter 1, we will introduce the definitions and the notations used throughout this thesis. We will also survey some prior research pertaining to graph decompositions, with special emphasis on star-decompositions and ...
• #### The number of (0,1) - Matrices with fixed row and column sums ﻿

(University of Waikato, 2013)
Let R and S be non-negative and non-increasing vectors of order m and n respectively. We consider the set A(R, S) of all m x n matrices with entries restricted to {0, 1}. We give an alternative proof of the Gale-Ryser ...