Geodesic
Partially-2-homogeneous monounary algebras
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 3, pp. 655-668.

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This paper is a continuation of [5], where $k$-homogeneous and $k$-set-homogeneous algebras were defined. The definitions are analogous to those introduced by Fraïssé [2] and Droste, Giraudet, Macpherson, Sauer [1] for relational structures. In [5] we found all 2-homogeneous and all 2-set-homogeneous monounary algebras when the homogenity is considered with respect to subalgebras, to connected subalgebras and with respect to connected partial subalgebras, respectively. The results of [3], where all homogeneous monounary algebras were characterized, were applied in [4] for 1-homogeneity. The aim of the present paper is to describe all monounary algebras which are 2-homogeneous and 2-set-homogeneous with respect to partial subalgebras, respectively; we will say that they are partially-2-homogeneous and partially-2-set-homogeneous.
Classification : 08A60
Keywords: monounary algebra; 2-homogeneous; 2-set-homogeneous; partially-2-homogeneous; partially-2-set-homogeneous 
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Jakubíková-Studenovská, Danica. Partially-2-homogeneous monounary algebras. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 3, pp. 655-668. http://geodesic.mathdoc.fr/item/CMJ_2003__53_3_a13/