Patterns in Permutations and Words

There has been considerable interest recently in the subject of patterns in permutations and words, a new branch of combinatorics with its roots in the works of Rotem, Rogers, and Knuth in the 1970s. Consideration of the patterns in question has been extremely interesting from the combinatorial point of view, and it has proved to be a useful language in a variety of seemingly unrelated problems, including the theory of Kazhdan—Lusztig polynomials, singularities of Schubert varieties, interval orders, Chebyshev polynomials, models in statistical mechanics, and various sorting algorithms, including sorting stacks and sortable permutations.

 

Lady Luck: The Theory of Probability

Everyday questions such as "Should I take my umbrella?" involve probability — a topic important in daily life and in science. This witty, nontechnical introduction to the subject elucidates such concepts as permutations, independent events, mathematical expectation, the law of averages and more. No advanced math required. 49 drawings.