Cancellation in cyclic consecutive systems

  • Authors:

  • Neil J. Calkin;Jonathan D. Edds;Douglas R. Shier

  • Affiliations:

  • Clemson University, Department of Mathematical Sciences, Clemson, South Carolina;Clemson University, Department of Mathematical Sciences, Clemson, South Carolina;Clemson University, Department of Mathematical Sciences, Clemson, South Carolina

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
  • Year:
  • 2002

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Abstract

We consider the structure and number of non-zero terms in the reliability polynomials for cyclic consecutive systems. We explain the large amount of cancellation, the fact that all but one of the coefficients are 0, 1 or -1, and show that the number of non-zero coefficients is asymptotic to αk, where α is the largest root of 2 + xr - xr-1 = 0.