Метод комбинаторики: Концепции, решенные примеры и упражнения для овладения искусством подсчета | Бижекции, включение-исключение, числа Каталана, генерирующие функции, принцип Бёрнсайда и Поля

Why do so many seemingly different problems -- monotonic lattice paths, valid parenthesizations, binary trees, polygon triangulations -- all reduce to the same number? Why is a bijective argument often more convincing than an algebraic one? How can a simple formal power series solve a recurrence in a few lines? Combinatorics answers these questions, and it does so with a rare elegance. This book is built to take you from the first counting principle to the most powerful tools -- without unnecessary formalism, but without sacrificing rigor. Across 8 progressive chapters, you discover the art of counting (with every formula proven twice, by algebra and by a bijection), pigeonhole as a proof method rather than a trick, inclusion-exclusion and derangements, the Catalan universe that unifies an entire family of objects under one number, recurrence relations with a CS and algorithms framing, generating functions taught as a 5-step master technique, counting under symmetry via Burnside and Polya, and finally combinatorics in the wild. Each concept is introduced through worked examples and reinforced by targeted exercises whose solutions explain the method step by step. Whether you are preparing for olympiads or a competitive exam, shoring up your foundations before an algorithms or probability course, working in quantitative finance or operations research, or simply love mathematics for what it is -- this book is your entry point into modern combinatorics. A few chapters are enough to change the way you look at any counting problem.