Labeling the Nodes in the Intrinsic Order Graph with Their Weights

Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 229)

Abstract

This chapter deals with the study of some new properties of the intrinsic order graph. The intrinsic order graph is the natural graphical representation of a complex stochastic Boolean system (CSBS). A CSBS is a system depending on an arbitrarily large number \(n\) of mutually independent random Boolean variables. The intrinsic order graph displays its \(2^{n}\) vertices (associated to the CSBS) from top to bottom, in decreasing order of their occurrence probabilities. New relations between the intrinsic ordering and the Hamming weight (i.e., the number of \(1\)-bits in a binary \(n\)-tuple) are derived. Further, the distribution of the weights of the \(2^{n}\) nodes in the intrinsic order graph is analyzed.

Keywords

Complex stochastic Boolean systems Hamming weight  Intrinsic order Intrinsic order graph Subgraphs Subposets 

Notes

Acknowledgments

This work was supported in part by the “Ministerio de Economía y Competitividad” (Spanish Government), and FEDER, through Grant contract: CGL2011-29396-C03-01.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Research Institute IUSIANI, Department of MathematicsUniversity of Las Palmas de Gran CanariaLas Palmas de Gran CanariaSpain

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