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Criteria for the Height of an Atom

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Abstract

In this paper three criteria for the height of an atom in terms of its \(f\)-graph are established. The obstacles to the oriented embeddability of the \(f\)-graph into the plane are found. The combinatorial properties of labeled oriented cycles, which are a generalization of chord diagrams, are investigated.

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ACKNOWLEDGMENTS

The author thanks A. T. Fomenko and I. M. Nikonov for the problem formulation and attention to this work.

Funding

The work is supported by the Program of the President of the Russian Federation ‘‘Leading Scientific Schools of the Russian Federation’’ (grant no. NSh–6399.2018.1, agreement no. 075–02–2018–867) and by the Theoretical Physics and Mathematics Advancement Foundation ‘‘BASIS’’.

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Authors and Affiliations

  1. Chair of Differential Geometry and Applications, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    V. A. Trifonova

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  1. V. A. Trifonova
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Correspondence to V. A. Trifonova.

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Translated by E. Oborin

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Trifonova, V.A. Criteria for the Height of an Atom. Moscow Univ. Math. Bull. 75, 102–116 (2020). https://doi.org/10.3103/S0027132220030079

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