Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Upper Bound for Cancellative Pairs   A pair $(\mathcal{A},\mathcal{B})$ of families of subsets of an $n$-element
set is called cancellative if whenever $A,A'\in\mathcal{A}$ and
$B\in\mathcal{B}$ satisfy $A\cup B=A'\cup B$, then $A=A'$, and whenever
$A\in\mathcal{A}$ and $B,B'\in\mathcal{B}$ satisfy $A\cup B=A\cup B'$, then
$B=B'$. It is known that there exist cancellative pairs with
$|\mathcal{A}||\mathcal{B}|$ about $2.25^n$, whereas the best known upper bound
on this quantity is $2.3264^n$. In this paper we improve this upper bound to
$2.2682^n$. Our result also improves the best known upper bound for Simonyi's
sandglass conjecture for set systems.

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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics