Set Operads in Combinatorics and Computer Science

  • Miguel A. Méndez

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Miguel A. Méndez
    Pages 1-4
  3. Miguel A. Méndez
    Pages 5-8
  4. Miguel A. Méndez
    Pages 9-61
  5. Miguel A. Méndez
    Pages 63-94
  6. Miguel A. Méndez
    Pages 95-108
  7. Miguel A. Méndez
    Pages 109-123
  8. Back Matter
    Pages 125-129

About this book

Introduction

This monograph has two main objectives. The first one is to give a self-contained exposition of the relevant facts about set operads, in the context of combinatorial species and its operations. This approach has various advantages: one of them is that the definition of combinatorial operations on species, product, sum, substitution and derivative, are simple and natural. They were designed as the set theoretical counterparts of the homonym operations on exponential generating functions, giving an immediate insight on the combinatorial meaning of them. The second objective is more ambitious. Before formulating it, authors present a brief historic account on the sources of decomposition theory. For more than forty years decompositions of discrete structures have been studied in different branches of discrete mathematics: combinatorial optimization, network and graph theory, switching design or boolean functions, simple multi-person games and clutters, etc.

Keywords

Decomposition theory Decomposition tree Koszul operads Modular decomposition Set operads Simple multiperson games

Authors and affiliations

  • Miguel A. Méndez
    • 1
  1. 1.Department of MathematicsIVICSan Antonio de Los AltosVenezuela

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-11713-3
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-11712-6
  • Online ISBN 978-3-319-11713-3
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • About this book
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