Matthew Ashford

collaborators

2 papers

math.CO2016

Graphs of kei and their diameters

Matthew Ashford

A kei on $[n]$ can be thought of as a set of maps $(f_{x})_{x \in [n]}$ , where each $f_{x}$ is an involution on $[n]$ such that $(x) f_{x} = x$ for all $x$ and $f_{(x) f_{y}} = f_{y} f_{x} f_{y}$ fo…

math.CO2016

Counting racks of order n

Matthew Ashford, Oliver Riordan

A rack on $[n]$ can be thought of as a set of maps $(f_{x})_{x \in [n]}$ , where each $f_{x}$ is a permutation of $[n]$ such that $f_{(x) f_{y}} = f_{y}^{- 1} f_{x} f_{y}$ for all $x$ and $y$ . In 2…