Combinatorial Species

Combinatorial Species

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Description

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for analysing discrete structures in terms of generating functions. Examples of discrete structures are graphs, permutations, trees, and so on; each of these has an associated generating function which counts how many structures there are of a certain size. One goal of species theory is to be able to analyse complicated structures by describing them in terms of transformations and combinations of simpler structures. These operations correspond to equivalent manipulations of generating functions, so producing such functions for complicated structures is much easier than with other methods. The theory was introduced by Andr Joyal. The power of the theory comes from its level of abstraction. The "description format" of a structure is irrelevant, because species are purely algebraic. Category theory provides a useful language for the concepts that arise here, but it is not necessary to understand categories before being able to work with species.show more

Product details

  • Paperback | 112 pages
  • 152 x 229 x 7mm | 177g
  • Loc Publishing
  • United States
  • English
  • 6136616602
  • 9786136616605