Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Proof of the Strict Monotone 5-step Conjecture   A computer search through the oriented matroid programs with dimension 5 and
10 facets shows that the maximum strictly monotone diameter is 5. Thus
$\Delta_{sm}(5,10)=5$. This enumeration is analogous to that of Bremner and
Schewe for the non-monotone diameter of 6-polytopes with 12 facets. Similar
enumerations show that $\Delta_{sm}(4,9)=5$ and
$\Delta_m(4,9)=\Delta_m(5,10)=6.$ We shorten the known non-computer proof of
the strict monotone 4-step conjecture.

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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: nlin
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
28
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: cs
36
The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex