The combinatorics of frieze patterns and Markoff numbers

... model based on perfect matchings that explains the symmetries of the numerical arrays that Conway and Coxeter dubbed frieze patterns. This matchings model is a combinatorial interpretation of Fomin and Zelevinsky’s cluster algebras of type A. One can derive from the matchings model an enumerative meaning for the Markoff numbers, and prove that the associated Laurent polynomials have positive coefficients as was conjectured (much more generally) by Fomin and Zelevinsky. Most of this research was conducted under the auspices of REACH (Research Experiences in Algebraic Combinatorics at Harvard)

Person-centred healthcare research: a personal influence

This commentary assesses the contribution made by the person-centred healthcare research of McCormack et al (2017) to research methodology and our ability to evaluate an organisation’s claims to be person-centred. It discusses the importance of person-centred ethical approaches within rigorous research methodologies