Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ramsey theory over partitions II: Negative Ramsey relations and pump-up
  theorems   In this series of papers we advance Ramsey theory of colorings over
partitions. In this part, we concentrate on anti-Ramsey relations, or, as they
are better known, strong colorings, and in particular solve two problems from
[CKS21].
  It is shown that for every infinite cardinal $\lambda$, a strong coloring on
$\lambda^+$ by $\lambda$ colors over a partition can be stretched to one with
$\lambda^{+}$ colors over the same partition. Also, a sufficient condition is
given for when a strong coloring witnessing $Pr_1(\ldots)$ over a partition may
be improved to witness $Pr_0(\ldots)$.
  Since the classical theory corresponds to the special case of a partition
with just one cell, the two results generalize pump-up theorems due to Eisworth
and Shelah, respectively.

32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs