Patients with COPD attending PR in Australia have high rates of comorbidity. The number of medications prescribed for these individuals is similar to that seen in other chronic disease states such as chronic heart failure. Pulmonary rehabilitation presents opportunities for clinicians to educate patients on self-management strategies for multiple comorbidities, review medication usage, and discuss strategies aimed at optimizing adherence with medication regimes.
Abstract. We define and enumerate two new two-parameter permutation families, namely, placements of a maximum number of non-attacking rooks on k chained-together n × n chessboards, in either a circular or linear configuration. The linear case with k = 1 corresponds to standard permutations of n, and the circular case with n = 4 and k = 6 corresponds to a three-person chessboard. We give bijections of these rook placements to matrix form, one-line notation, and matchings on certain graphs. Finally, we define chained linear and circular alternating sign matrices, enumerate them for certain values of n and k, and give bijections to analogues of monotone triangles, square ice configurations, and fully-packed loop configurations.
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