Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattices with non-Shannon Inequalities   We study the existence or absence of non-Shannon inequalities for variables
that are related by functional dependencies. Although the power-set on four
variables is the smallest Boolean lattice with non-Shannon inequalities there
exist lattices with many more variables without non-Shannon inequalities. We
search for conditions that ensures that no non-Shannon inequalities exist. It
is demonstrated that 3-dimensional distributive lattices cannot have
non-Shannon inequalities and planar modular lattices cannot have non-Shannon
inequalities. The existence of non-Shannon inequalities is related to the
question of whether a lattice is isomorphic to a lattice of subgroups of a
group.

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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th