Abstract view
A Note on a Conjecture of S. Stahl


Published:20080801
Printed: Aug 2008
Abstract
S. Stahl (Canad. J. Math. \textbf{49}(1997), no. 3, 617640)
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.
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]
