Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Lower Bound for van der Waerden Numbers   In this paper we prove a new recurrence relation on the van der Waerden
numbers, $w(r,k)$. In particular, if $p$ is a prime and $p\leq k$ then $w(r, k)
> p \cdot \left(w\left(r - \left\lceil \frac{r}{p}\right\rceil, k\right)
-1\right)$. This recurrence gives the lower bound $w(r, p+1) > p^{r-1}2^p$ when
$r \leq p$, which generalizes Berlekamp's theorem on 2-colorings, and gives the
best known bound for a large interval of $r$. The recurrence can also be used
to construct explicit valid colorings, and it improves known lower bounds on
small van der Waerden numbers.

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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-ex
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph