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Objective Identify key features of an enduring group exercise program for people with Parkinson’s disease (PD) by exploring experiences of participants, student assistants and the exercise instructor through a convergent mixed methods design. Methods Fourteen people with PD (modified Hoehn & Yahr: 1–3.5) who regularly participated in a group exercise program (≥ 50% of classes for ≥ 1 year) were interviewed to explore their perceptions of the program. The exercise instructor was also interviewed and weekly written reflections were collected from 18 undergraduate student assistants. Using a grounded theory approach, interviews and written reflections were thematically analyzed via qualitative content analysis. Quantitative data from the Physical Fitness and Exercise Activity Levels of Older Adults Scale were used as part of a convergent mixed-methods design to move towards theory formation. Results Thematic analysis of the PD participant interviews revealed 4 themes: 1) Quality of the program, 2) Social interactions, 3) Facilitators to exercise, 4) Barriers to exercise. The exercise instructor interview revealed 2 themes: individualization and functionality of exercises, and creating a nurturing atmosphere. Themes from students’ data included student learning, and positive in-class experiences. Means (sd) were 1.6 (0.5) for facilitators and 3.0 (0.5) for barriers subscales (1=strongly agree to 4=strongly disagree). Conclusion These varied sources of data converge to identify and characterize key features of an enduring group exercise program for people with PD: a positive and nurturing environment, varied and individually tailored exercise content, and the importance of social cohesion. These findings also highlight the critical role of multiple stakeholders in fostering an environment that facilitates long-term adherence to group exercise.

We present two extensions of the linear bound, due to Marcus and Tardos, on the number of 1-entries in an nxn(0,1)-matrix avoiding a fixed permutation matrix. We first extend the linear bound to hypergraphs with ordered vertex sets and, using previous results of Klazar, we prove an exponential bound on the number of hypergraphs on n vertices which avoid a fixed permutation. This, in turn, solves various conjectures of Klazar as well as a conjecture of Branden and Mansour. We then extend the original Furedi-Hajnal problem from ordinary matrices to d-dimensional matrices and show that the number of 1-entries in a d-dimensional (0,1)-matrix with side length n which avoids a d-dimensional permutation matrix is O(n^d^-^1).