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Appendix A - AUXILIARY ELEMENTARY NOTIONS

from Part D - APPENDICES

Published online by Cambridge University Press:  11 April 2011

Philippe Flajolet
Affiliation:
Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt
Robert Sedgewick
Affiliation:
Princeton University, New Jersey
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Summary

We combine in the three appendices definitions and theorems related to key mathematical concepts not covered directly in the text. Generally, the entries in the appendices are independent, intended for reference while addressing the main text. Our own Introduction to the Analysis of Algorithms [538] is a gentle introduction to many of the concepts underlying analytic combinatorics at a level accessible to any college student and is reasonable preparation for undergraduates or anyone undertaking to read this book for self-study.

This appendix contains entries that are arranged in alphabetical order, regarding the following topics:

Arithmetical functions; Asymptotic notations; Combinatorial probability; Cycle construction; Formal power series; Lagrange inversion; Regular languages; Stirling numbers; Tree concepts.

The corresponding notions and results are used throughout the book, and especially in Part A relative to Symbolic Methods. Accessible introductions to the subject of this appendix are the books by Graham–Knuth–Patashnik [307], and Wilf [608], regarding combinatorial enumeration, and De Bruijn's vivid booklet [142], regarding asymptotic analysis. Reference works in combinatorial analysis are the books by Comtet [129], Goulden–Jackson [303], and Stanley [552, 554].

Arithmetical functions

A general reference for this section is Apostol's book [16]. First, the Euler totient function ϕ(k) intervenes in the unlabelled cycle construction (pp. 27, 84, 165, as well as 729 below). It is defined as the number of integers in [1 ‥ k] that are relatively prime to k.

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Publisher: Cambridge University Press
Print publication year: 2009

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  • AUXILIARY ELEMENTARY NOTIONS
  • Philippe Flajolet, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt, Robert Sedgewick, Princeton University, New Jersey
  • Book: Analytic Combinatorics
  • Online publication: 11 April 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511801655.012
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  • AUXILIARY ELEMENTARY NOTIONS
  • Philippe Flajolet, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt, Robert Sedgewick, Princeton University, New Jersey
  • Book: Analytic Combinatorics
  • Online publication: 11 April 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511801655.012
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • AUXILIARY ELEMENTARY NOTIONS
  • Philippe Flajolet, Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt, Robert Sedgewick, Princeton University, New Jersey
  • Book: Analytic Combinatorics
  • Online publication: 11 April 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511801655.012
Available formats
×