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A Note on a Conjecture of S. Stahl

  Published:2008-08-01
 Printed: Aug 2008
  • Yichao Chen
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Abstract

S. Stahl (Canad. J. Math. \textbf{49}(1997), no. 3, 617--640) conjectured that the zeros of genus polynomial are real. L. Liu and Y. Wang disproved this conjecture on the basis of Example 6.7. In this note, it is pointed out that there is an error in this example and a new generating matrix and initial vector are provided.
Keywords: genus polynomial, zeros, real genus polynomial, zeros, real
MSC Classifications: 05C10, 05A15, 30C15, 26C10 show english descriptions Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]
Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10}
Polynomials: location of zeros [See also 12D10, 30C15, 65H05]
05C10 - Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]
05A15 - Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
30C15 - Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10}
26C10 - Polynomials: location of zeros [See also 12D10, 30C15, 65H05]
 

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