Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A graph-theoretic approach to a conjecture of Dixon and Pressman   Given $n \times n$ matrices, $A_1, \dots, A_k$, consider the linear operator
$L(A_1,\dots,A_k) \, \colon \; \operatorname{M}_n \to \operatorname{M}_n$ given
by \[ L(A_1,\dots,A_k)(A_{k+1})= \sum_{\sigma\in S_{k+1}}
\operatorname{sign}(\sigma) A_{\sigma(1)}A_{\sigma(2)} \cdots A_{\sigma(k+1)}.
\] The Amitsur-Levitzki theorem asserts that $L(A_1, \ldots, A_k)$ is
identically $0$ for every $k \geq 2n-1$. Dixon and Pressman conjectured that if
$k$ is an even number between $2$ and $2n - 2$, then the kernel of $L(A_1,
\ldots, A_k)$ is of dimension $k$ for $A_1, \ldots, A_k\in
\operatorname{M}_n(\mathbb{R})$ in general position. We prove this conjecture
using graph-theoretic techniques.

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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an