Combinatorics of permutations

Abstract

In One Line and Close. Permutations as Linear Orders. Descents Alternating Runs Alternating Subsequences In One Line and Anywhere. Permutations as Linear Orders. Inversions. Inversions Inversion in Permutations of Multisets In Many Circles. Permutations as Products of Cycles. Decomposing a Permutation into Cycles Type and Stirling Numbers Cycle Decomposition versus Linear Order Permutations with Restricted Cycle Structure In Any Way but This. Pattern Avoidance. The Basics. The Notion of Pattern Avoidance Patterns of Length Three Monotone Patterns Patterns of Length Four The Proof of the Stanley-Wilf Conjecture In This Way but Nicely. Pattern Avoidance. Follow-Up. Polynomial Recurrences Containing a Pattern Many Times Containing a Pattern a Given Number of Times Mean and Insensitive. Random Permutations. The Probabilistic Viewpoint Expectation Variance and Standard Deviation An Application: Longest Increasing Subsequences Permutations versus Everything Else. Algebraic Combinatorics of Permutations. The Robinson-Schensted-Knuth Correspondence Posets of Permutations Simplicial Complexes of Permutations Get Them All. Algorithms and Permutations. Generating Permutations Stack Sorting Permutations Variations of Stack Sorting How Did We Get Here? Permutations as Genome Rearrangements. Introduction Block Transpositions Block Interchanges Block Transpositions Revisited Solutions to Odd-Numbered Exercises References List of Frequently Used Notation Index Exercises, Problems, and Problem Solutions appear at the end of each chapter.