Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jumps in speeds of hereditary properties in finite relational languages   Given a finite relational language $\mathcal{L}$, a hereditary
$\mathcal{L}$-property is a class of finite $\mathcal{L}$-structures closed
under isomorphism and substructure. The speed of $\mathcal{H}$ is the function
which sends an integer $n\geq 1$ to the number of distinct elements in
$\mathcal{H}$ with underlying set $\{1, . . . , n\}$. In this paper we give a
description of many new jumps in the possible speeds of a hereditary
$\mathcal{L}$-property, where $\mathcal{L}$ is any finite relational language.
In particular, we characterize the jumps in the polynomial and factorial
ranges, and show they are essentially the same as in the case of graphs. The
results in the factorial range are new for all examples requiring a language of
arity greater than two, including the setting of hereditary properties of
$k$-uniform hypergraphs for $k>2$. Further, adapting an example of Balogh,
Bollob\'{a}s, and Weinreich, we show that for all $k\geq 2$, there are
hereditary properties of $k$-uniform hypergraphs whose speeds oscillate between
functions near the upper and lower bounds of the penultimate range, ruling out
many natural functions as jumps in that range. Our theorems about the factorial
range use model theoretic tools related to the notion of mutual algebricity.

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The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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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: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex