International Journal of Theoretical and Applied Mathematics

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Combinatorial Structures to Construct Simple Games and Molecules

Received: 28 October 2016    Accepted: 12 January 2017    Published: 02 March 2017
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Abstract

We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-) heuristics algorithms and parallel programming, among others.

DOI 10.11648/j.ijtam.20170302.16
Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 2, April 2017)
Page(s) 82-87
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Combinatorial Structures, Generating Simple Games, Generating Influence Games, Generating Molecules

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Author Information
  • Department of Mathematics, Universitat Politècnica de Catalunya, Manresa, Spain

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    Xavier Molinero. (2017). Combinatorial Structures to Construct Simple Games and Molecules. International Journal of Theoretical and Applied Mathematics, 3(2), 82-87. https://doi.org/10.11648/j.ijtam.20170302.16

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    ACS Style

    Xavier Molinero. Combinatorial Structures to Construct Simple Games and Molecules. Int. J. Theor. Appl. Math. 2017, 3(2), 82-87. doi: 10.11648/j.ijtam.20170302.16

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    AMA Style

    Xavier Molinero. Combinatorial Structures to Construct Simple Games and Molecules. Int J Theor Appl Math. 2017;3(2):82-87. doi: 10.11648/j.ijtam.20170302.16

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  • @article{10.11648/j.ijtam.20170302.16,
      author = {Xavier Molinero},
      title = {Combinatorial Structures to Construct Simple Games and Molecules},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {3},
      number = {2},
      pages = {82-87},
      doi = {10.11648/j.ijtam.20170302.16},
      url = {https://doi.org/10.11648/j.ijtam.20170302.16},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijtam.20170302.16},
      abstract = {We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-) heuristics algorithms and parallel programming, among others.},
     year = {2017}
    }
    

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    AB  - We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-) heuristics algorithms and parallel programming, among others.
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