Combinatorial Structures to Construct Simple Games and Molecules

Xavier Molinero

doi:doi:10.11648/j.ijtam.20170302.16

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Combinatorial Structures to Construct Simple Games and Molecules

Xavier Molinero

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 2)

Received: 28 October 2016 Accepted: 12 January 2017 Published: 2 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.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 2)
DOI	10.11648/j.ijtam.20170302.16
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), 2017. Published by Science Publishing Group

Keywords

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

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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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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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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - Combinatorial Structures to Construct Simple Games and Molecules
AU  - Xavier Molinero
Y1  - 2017/03/02
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170302.16
DO  - 10.11648/j.ijtam.20170302.16
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 82
EP  - 87
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170302.16
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.
VL  - 3
IS  - 2
ER  -

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Author Information

Xavier Molinero

Department of Mathematics, Universitat Politècnica de Catalunya, Manresa, Spain

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APA Style

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

Copy | Download

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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Combinatorial Structures to Construct Simple Games and Molecules
AU  - Xavier Molinero
Y1  - 2017/03/02
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170302.16
DO  - 10.11648/j.ijtam.20170302.16
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 82
EP  - 87
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170302.16
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.
VL  - 3
IS  - 2
ER  -

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