Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Boolean Rainbow Ramsey Number of Antichains, Boolean Posets, and
  Chains   Motivated by the paper of Axenovich and Walzer [2], we study the Ramsey-type
problems on the Boolean lattices. Given posets $P$ and $Q$, we look for the
smallest Boolean lattice $\mathcal{B}_N$ such that any coloring on elements of
$\mathcal{B}_N$ must contain a monochromatic $P$ or a rainbow $Q$. This number
$N$ is called the Boolean rainbow Ramsey number of $P$ and $Q$ in the paper.
  Particularly, we determine the exact values of the Boolean rainbow Ramsey
number for $P$ and $Q$ being the antichains, the Boolean posets, or the chains.
From these results, we also give some general upper and lower bounds of the
Boolean rainbow Ramsey number for general $P$ and $Q$ in terms of the poset
parameters.

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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph