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  • © 2015

Set Operads in Combinatorics and Computer Science

Authors:

  • Gives a detailed elementary introduction to set operads from the point of view of species, the advantages of this approach are explained in the abstract
  • Settles decomposition theory in to the area of domain of a very general and powerful machinery: set operads and operads in general
  • Would be of the interest to computer scientists as well as to the operadic community
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH, volume 0)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xv
  2. Introduction

    • Miguel A. Méndez
    Pages 1-4
  3. Preliminaries on Species and Set Operads

    • Miguel A. Méndez
    Pages 5-8
  4. Operations on Species and Operads

    • Miguel A. Méndez
    Pages 9-61
  5. Decomposition Theory

    • Miguel A. Méndez
    Pages 63-94
  6. Rigid Operads

    • Miguel A. Méndez
    Pages 95-108
  7. Posets from Cancellative Operads and Koszul Duality

    • Miguel A. Méndez
    Pages 109-123
  8. Back Matter

    Pages 125-129

About this book

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.

Authors and Affiliations

  • Department of Mathematics, IVIC, San Antonio de Los Altos, Venezuela

    Miguel A. Méndez

Bibliographic Information

  • Book Title: Set Operads in Combinatorics and Computer Science

  • Authors: Miguel A. Méndez

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-11713-3

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Author(s) 2015

  • Softcover ISBN: 978-3-319-11712-6Published: 21 January 2015

  • eBook ISBN: 978-3-319-11713-3Published: 08 January 2015

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: XV, 129

  • Number of Illustrations: 19 b/w illustrations, 43 illustrations in colour

  • Topics: Special Functions, Complex Systems, Operator Theory

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access