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Search: MSC category 26C10 ( Polynomials: location of zeros [See also 12D10, 30C15, 65H05] )

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1. CJM 2008 (vol 60 pp. 958)

Chen, Yichao
A Note on a Conjecture of S. Stahl
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
Categories:05C10, 05A15, 30C15, 26C10

2. CJM 2008 (vol 60 pp. 960)

3. CJM 1997 (vol 49 pp. 617)

Stahl, Saul
On the zeros of some genus polynomials
In the genus polynomial of the graph $G$, the coefficient of $x^k$ is the number of distinct embeddings of the graph $G$ on the oriented surface of genus $k$. It is shown that for several infinite families of graphs all the zeros of the genus polynomial are real and negative. This implies that their coefficients, which constitute the genus distribution of the graph, are log concave and therefore also unimodal. The geometric distribution of the zeros of some of these polynomials is also investigated and some new genus polynomials are presented.

Categories:05C10, 05A15, 30C15, 26C10

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