Strictly balanced uniform hypergraphs and generalizations of Zero-One Law |
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| Institution: | 1. Moscow Institute of Physics and Technology, Laboratory of Advanced Combinatorics and Network Applications, Russian Federation;2. Moscow State University, Laboratory of Advanced Combinatorics and Network Applications, Russian Federation;3. National Research University Higher School of Economics, Russian Federation |
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| Abstract: | In this work we describe the spectra of all rational numbers that could be a density of a strictly balanced uniform hypergraph. We also introduce some specific constructions of strictly balanced uniform hypergraphs, and exploit them to generalize some results about Zero-One Law and Zero-One k-Law to the case of random uniform hypergraphs. |
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| Keywords: | Strictly balanced hypergraph Random hypergraph First-order logic Zero-One Law |
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