Enumerative combinatorics applications in Computer Science I am interested in specific examples and applications of enumerative combinatorics in Computer Science -- concrete problems in this field that make explicit use of the concepts and ideas from combinatorics. Are there any good references that you can point me to (books, lectures, ...)?
 A: 
A little treasure is the  30 years old Mathematics for the Analysis of Algorithms by D.E. Knuth and D.H. Greene.



*

*From the preface: ... Much of the material is drawn from the starred sections of The Art of  Computer Programming, Volume 3.
Analysis of algorithms, as a discipline, relies heavily on both computer science and mathematics. This report is a mathematical look at the synthesis - emphasizing the mathematical perspective, but using motivation and examples from computer science.
It covers binomial identities, recurrence relations, operator methods and asymptotic analysis, ...
Many years ago when I studied computer science I was fascinated about the cool    Cookie Monster, used to analyse hashing and introduced in section 3.1. In fact nearly each section from this book we've studied in a combinatorics seminar had this wow - effect.
A: A very attractive book, with a virtuous teaching and excellent references on this topic is "Combinatorial Enumerative"                  (in Spanish), written by the mathematician of Costa Rica, Eduardo Piza Volio, Editorial of the University of Costa Rica (2003). 
                    I attached bibliography in which there are other references.

A: Maybe you can help this book:

Enumerative Combinatorics by Richard P. Stanley 
  Download as pdf

Other interesting books:
Principles and Techniques in Combinatorics by Chen Chuan-Chong and Koh Khee-Meng  More info - Download as pdf
Combinatorics and Graph Theory (2nd edition) by John Harris, Jeffry L. Hirst, and Michael Mossinghoff - More info - Download as pdf
Combinatorics by RUSSELL MERRIS, California State University, Hayward
Download as pdf
A: A trick that I've been employing on several occasions is ternary number base enumeration:

Contours & Isosurfaces

The area of the region $|x-ay|\le c$ for $0\le x\le 1$ and $0\le y\le 1$

Quite a limited scope, but very useful.
A: The emphasis  is on enumeration  rather than counting if  I understand
the question correctly. The  perfect match would be the combstruct
package that is  included with Maple. This software  is a companion to
the book  Analytical Combinatorics by Flajolet  and Sedgewick, which
is the canonical text and  basically provides a map of future computer
science  research for  decades to  come. Highly  recommended. Computer
science  has a  particular focus  on trees  and  combstruct really
shines  here,  providing  total  enumeration  as  well  as  generating
functions and functional equations.  The landmark paper by Flajolet et
al. on  random mapping  statistics (which are  closely related  to the
labeled    tree    function)     is    discussed    at    this    MSE
link.    The  Maple
package    is    used   the    following    MSE   combstruct    link,
I   and  this  MSE
combstruct                                                        link,
II.     The    book
Analytical Combinatorics  is unprecedented in that  it pioneered the
use  of complex variable  methods to  treat generating  functions that
arise from  species theory and  the folklore theorem  of combinatorial
enumeration (providing  instant translation from  species equations to
generating  functions),  thereby   putting  an  emphasis  on  unifying
combinatorial  methods  with  complex  variable  techniques.   Another
relevant early text is the  book Graphical Enumeration by Harary and
Palmer which contains  many results on labeled and  unlabeled trees as
well as accessible presentations  of the Polya Enumeration Theorem and
of  Power Group  Enumeration.   Finally a  classic  contender for  the
enumeration of  unlabeled trees is  the NAUTY package by  McKay, which
was          used         at          this          MSE         NAUTY
link. (Use  Pruefer
codes for labeled trees.)
