Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distinct monomial orders with same induced orderings   We prove that the lexicographic, degree lexicographic and the degree reverse
lexicographic orders for monomials in $R_n=K[X_1,...X_n]$ are uniquely
determined by their induced orderings, (i.e. their restrictions to
$R_{n,i}=K[X_1,..., \hat{X_i}, .., X_n]$), when $n \geq 4$. We also show that
for any $n \geq 4$ there are monomial orders that are not uniquely determined
by their induced orderings, and provide examples of these orders for each $n$.

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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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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: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin