Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gowers' Ramsey theorem for generalized tetris operations   We prove a generalization of Gowers' theorem for $\mathrm{FIN}_{k}$ where,
instead of the single tetris operation $T:\mathrm{FIN}_{k}\rightarrow
\mathrm{FIN}_{k-1}$, one considers all maps from $\mathrm{FIN}_{k}$ to
$\mathrm{FIN}_{j}$ for $0\leq j\leq k$ arising from nondecreasing surjections
$f:\left\{ 0,1,\ldots ,k+1\right\} \rightarrow \left\{ 0,1,\ldots ,j+1\right\}
$. This answers a question of Barto\v{s}ov\'{a} and Kwiatkowska. We also prove
a common generalization of such a result and the Galvin--Glazer--Hindman
theorem on finite products, in the setting of layered partial semigroups
introduced by Farah, Hindman, and McLeod.

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The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
19
The categories of this paper are: eess
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The categories of this paper are: acc-phys
18
The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
8
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: nucl-th