Compressed Representations of Permutations, and Applications

We explore various techniques to compress a permutation $\pi$ over n integers, taking advantage of ordered subsequences in $\pi$, while supporting its application $\pi$(i) and the application of its inverse $\pi^{-1}(i)$ in small time. Our compression schemes yield several interesting byproducts, in many cases matching, improving or extending the best existing results on applications such as the encoding of a permutation in order to support iterated applications $\pi^k(i)$ of it, of integer functions, and of inverted lists and suffix arrays

Getting Students Excited about Data Analysis

The Graphing Art Project encourages students to explore functions as they create art. Students write functions with domain and range restrictions that generate interesting pictures. The project is easily tailored for different levels of mathematical learners. Algebra 1 students create art using linear functions; precalculus students include conic sections, exponential, logarithmic, trigonometric functions and the greatest integer functions in their work. Students may write graphing calculator programs to reproduce and animate their art