On the cardinality of layers in even-valued n-dimensional lattice

T.V. Andreeva^a∗ , Yu.S. Semenov^b∗∗

^aBauman Moscow State Technical University, Moscow, 105005 Russia

^bIndependent Researcher, Moscow, 111399 Russia

E-mail: ^∗t-v-andreeva@mail.ru, ^∗∗yurisemenoff@mail.ru

Received October 19, 2021

ORIGINAL ARTICLE

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DOI: 10.26907/2541-7746.2022.2-3.153-169

For citation: Andreeva T.V., Semenov Yu.S. On the cardinality of layers in even-valued n-dimensional lattice. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2022, vol. 164, no. 2–3, pp. 153–169. doi: 10.26907/2541-7746.2022.2-3.153-169. (In Russian)

Abstract

In this article, we explicitly calculated terms additional to the main one of cardinality asymptotics of central layers in the n-dimensional k-valued lattice E_kⁿ for even k as n → ∞. The main term had been found by V.B. Alekseev for a certain class of posets. The case of odd k , which is technically less complicated, was the major focus of our previous work.

Keywords: poset, layer, asymptotics, generating function

References

1. Andreeva T.V., Semenov Yu.S. On the cardinality of layers in some partially ordered sets. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2020, vol. 162, no. 3, pp. 269–284. doi: 10.26907/2541-7746.2020.3.269-284. (In Russian)
2. Alekseev V.B. On the number of k -valued monotone functions. Probl. Kibern., 1974, no. 28, pp. 5–24. (In Russian)
3. Dwight H.B. Tablitsy integralov i drugie matematicheskie formuly [Tables of Integrals and Other Mathematical Data]. Moscow, Nauka, 1978. 224 p. (In Russian)

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