Christopher Tuffley
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View article: Monadic transductions and definable classes of matroids
Monadic transductions and definable classes of matroids Open
A transduction provides us with a way of using the monadic second-order language of a structure to make statements about a derived structure. Any transduction induces a relation on the set of these structures. This article presents a self-…
View article: The rack congruence condition and half congruences in racks
The rack congruence condition and half congruences in racks Open
Racks and quandles are algebraic structures with a single binary operation that is right self-distributive and right invertible, and additionally idempotent in the case of quandles. The invertibility condition is equivalent to the existenc…
View article: IUM1: Indigenising University Mathematics Symposium, September 20–21, 2021
IUM1: Indigenising University Mathematics Symposium, September 20–21, 2021 Open
What does it mean to indigenise mathematics education
View article: Weakly Linked Embeddings of Pairs of Complete Graphs in $\mathbb{R}^3$
Weakly Linked Embeddings of Pairs of Complete Graphs in $\mathbb{R}^3$ Open
Let $G$ and $H$ be disjoint embeddings of complete graphs $K_m$ and $K_n$ in $\mathbb{R}^3$ such that some cycle in $G$ links a cycle in $H$ with non-zero linking number. We say that $G$ and $H$ are weakly linked if the absolute value of t…
View article: Parametric study of E. coli incidence with reference to the New Zealand freshwater standards and the Manawatū–Whanganui region
Parametric study of E. coli incidence with reference to the New Zealand freshwater standards and the Manawatū–Whanganui region Open
The New Zealand National Policy Statement for Freshwater Management 2020 sets several targets for freshwater quality, six of which are measurements of rivers; others relate to lakes. Each regional council is required to monitor freshwater …
View article: Parametric study of E. coli incidence with reference to the New Zealand freshwater standards and the Manawatū-Whanganui region
Parametric study of E. coli incidence with reference to the New Zealand freshwater standards and the Manawatū-Whanganui region Open
The New Zealand National Policy Statement for Freshwater Management 2020 sets several targets for freshwater quality, six of which are measurements of rivers; others relate to lakes. Each regional council is required to monitor freshwater …
View article: Weakly linked embeddings of pairs of complete graphs in $\mathbb{R}^3$
Weakly linked embeddings of pairs of complete graphs in $\mathbb{R}^3$ Open
Let $G$ and $H$ be disjoint embeddings of complete graphs $K_m$ and $K_n$ in $\mathbb{R}^3$ such that some cycle in $G$ links a cycle in $H$ with non-zero linking number. We say that $G$ and $H$ are *weakly linked* if the absolute value of…
View article: Intrinsic linking with linking numbers of specified divisibility
Intrinsic linking with linking numbers of specified divisibility Open
Let $n$, $q$ and $r$ be positive integers, and let $K_N^n$ be the $n$-skeleton of an $(N-1)$-simplex. We show that for $N$ sufficiently large every embedding of $K_N^n$ in $\mathbb{R}^{2n+1}$ contains a link $L_1\cup\cdots\cup L_r$ consist…
View article: Characterisation and classification of signatures of spanning trees of the $n$-cube
Characterisation and classification of signatures of spanning trees of the $n$-cube Open
The signature of a spanning tree $T$ of the $n$-cube $Q_n$ is the $n$-tuple $\mathrm{sig}(T)=(a_1,a_2,\dots,a_n)$ such that $a_i$ is the number of edges of $T$ in the $i$th direction. We characterise the $n$-tuples that can occur as the si…