Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Log-concavity of the genus polynomials of Ringel ladders   A Ringel ladder can be formed by a self-bar-amalgamation operation on a
symmetric ladder, that is, by joining the root vertices on its end-rungs. The
present authors have previously derived criteria under which linear chains of
copies of one or more graphs have log-concave genus polynomials. Herein we
establish Ringel ladders as the first significant non-linear infinite family of
graphs known to have log-concave genus polynomials. We construct an algebraic
representation of self-bar-amalgamation as a matrix operation, to be applied to
a vector representation of the partitioned genus distribution of a symmetric
ladder. Analysis of the resulting genus polynomial involves the use of
Chebyshev polynomials. This paper continues our quest to affirm the
quarter-century-old conjecture that all graphs have log-concave genus
polynomials.

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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph