Combinatorial Species and Tree-like Structures

Encyclopedia of Mathematics and its Applications #67

by François Bergeron, Gilbert Labelle, Pierre Leroux

The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labeled and unlabeled structures as well as a tool for the specification and analysis of these structures. This key reference presents the basic elements of the theory and gives a unified account of its developments and applications. The authors offer a modern introduction to the use of various generating functions, with applications to graphical enumeration, Polya Theory and analysis of data structures in computer science, and to other areas such as special functions, functional equations, asymptotic analysis, and differential equations.

Genres: Mathematics

Hardcover

First published January 1, 1997

Reviews

[Michael]

"It is primarily through experience that the combinatorial significance of the algebraic operations of [formal power series] is understood, as well as the problem of whether to use ordinary or exponential generating functions."
- Stanley's Enumerative Combinatorics

While I'm sure experience helps, all this can be made precise in the theory of species, which really illuminates things.

Unfortunately I've had to set this book aside for now because of, you know, my actual classes. But hopefully I will come back before long and finish this book, which I've really enjoyed so far.

[Ji · Rating 5 out of 5]

This is the book the inspired me to write my thesis. Therefore, it was my bible for a few years in my life.