Combinatorics of Permutations, 2nd Edition

Foreword

Permutations have a remarkably rich combinatorial structure. Part of the

reason for this is that a permutation of a finite set can be represented in many

equivalent ways, including as a word (sequence), a function, a collection of dis-

joint cycles, a matrix, etc. Each of these representations suggests a host of nat-

ural invariants (or “statistics”), operations, transformations, structures, etc.,

that can be applied to or placed on permutations. The fundamental statis-

tics, operations, and structures on permutations include descent set (with

numerous specializations), excedance set, cycle type, records, subsequences,

composition (product), ...