On growth function of finite rigid lattices
The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 2, pp. 124-133 Cet article a éte moissonné depuis la source Math-Net.Ru

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Rigid lattices, i.e., lattices, any its endomorphism is a constant endomorphism (mapping all elements to a some single element) or the identity endomorphism, are investigated. It is proved that the growth function of finite rigid lattices is exponential.
Keywords: lattice, rigid lattice, growth function.
Mots-clés : endomorphism
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O. E. Perminova. On growth function of finite rigid lattices. The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 2, pp. 124-133. http://geodesic.mathdoc.fr/item/IIGUM_2011_4_2_a9/

[1] F. Kharari, E. Palmer, Perechislenie grafov, Mir, M., 1977, 324 pp. | MR

[2] V. I. Trofimov, Funktsii rosta algebraicheskikh sistem, Avtoref. dis. ... kand. fiz.-mat. nauk, NGU, Novosibirsk, 1982, 10 pp.

[3] W. Klotz, L. Lucht, “Endliche Verbande”, J. Reine Angew. Math., 247 (1971), 58–68 | MR | Zbl

[4] E. A. Perminov, O zhestkikh reshetkakh, Dep. v VINITI 27.01.84, No 847-84, Ural. gos. un-t, 22 pp. | Zbl

[5] O. E. Perminova, “O konechnykh kriticheskikh reshetkakh”, Tr. In-ta matematiki i mekhaniki UrO RAN, 15, no. 2, 2009, 185–193 | MR

[6] Yu. M. Vazhenin, E. A. Perminov, “O zhestkikh reshetkakh i grafakh”, Issled. po sovrem. algebre, mezhvuz. sb. st., Matem. zapiski, 2, no. 3, Sverdlovsk, 1979, 3–21 | MR

[7] G. Grettser, Obschaya teoriya reshetok, Mir, M., 1981, 456 pp. | MR

[8] P. Crawley, R. P. Dilworth, Algebraic theory of lattices, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1973, 193 pp. | Zbl