Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Log-convexity and the cycle index polynomials with relation to compound
  Poisson distributions   We extend the exponential formula by Bender and Canfield (1996), which
relates log-concavity and the cycle index polynomials. The extension clarifies
the log-convexity relation. The proof is by noticing the property of a compound
Poisson distribution together with its moment generating function. We also give
a combinatorial proof of extended "log-convex part" referring Bender and
Canfield's approach, where the formula by Bruijn and Erd\"os (1953) is
additionally exploited. The combinatorial approach yields richer structural
results more than log-convexity. Furthermore, we consider normal and binomial
convolutions of sequences which satisfy the exponential formula. The operations
generate interesting examples which are not included in well known laws about
log-concavity/convexity.

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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs