30 citations · 132 across the 31 of their papers we have counts for
5 papers · 1 filter
A Language Hierarchy of Binary Relations
Tara Brough, Alan J. Cain
Motivated by the study of word problems of monoids, we explore two ways of viewing binary relations on as languages. We exhibit a hierarchy of classes of binary relations on…
Two applications of monoid actions to cross-sections
Tara Brough, Alan J. Cain, Victor Maltcev
Using a construction that builds a monoid from a monoid action, this paper exhibits an example of a direct product of monoids that admits a prefix-closed regular cross-section, but…
Conjugacy in Patience Sorting monoids
Alan J. Cain, António Malheiro, Fábio M. Silva
The cyclic shift graph of a monoid is the graph whose vertices are the elements of the monoid and whose edges connect elements that are cyclic shift related. The Patience Sorting a…
Visual thinking and simplicity in proof
Alan J. Cain
This paper studies how spatial thinking interacts with simplicity in [informal] proof, by analysing a set of example proofs mainly concerned with Ferrers diagrams (visual represent…
Combinatorics of patience sorting monoids
Alan J. Cain, António Malheiro, Fábio M. Silva
This paper makes a combinatorial study of the two monoids and the two types of tableaux that arise from the two possible generalizations of the Patience Sorting algorithm from perm…