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We extend a well-known relationship between the representation of the symmetric group on the homology of the partition lattice and the free Lie algebra to Dowling lattices.
A Grünbaum coloring of a triangulation is an assignment of colors to edges so that the edges about each face are assigned unique colors. In this paper we examine the color induced subgraphs given by a Grünbaum coloring of a triangulation and show that the existence of connected color induced subgraphs is equivalent to the Three Color Theorem. A… (More)
We prove a Ramsey-theoretic result on set partitions of finite sets and a refinement based on the number of blocks in the set partition. A well-known bijection shows that our results are equivalent to results on finite sequences in the spirit of the Erd˝ os-Szekeres theorem. 1. Background and Definitions In their early work on Ramsey theory, Erd˝ os and… (More)
OBJECTIVE The purpose of this study was to determine whether mobility and physical activity were associated with lung function in adults with cystic fibrosis (CF). DESIGN This was a prospective cohort observational study in an urban, academic, specialized care center. Participants were ambulatory, nonhospitalized adults with CF. MAIN OUTCOME MEASURES… (More)