Previous |  Up |  Next


monounary algebra; 2-homogeneous; 2-set-homogeneous; partially-2-homogeneous; partially-2-set-homogeneous
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.
[1] M.  Droste, M.  Giraudet, H. D.  Macpherson and N.  Sauer: Set-homogeneous graphs. J.  Combin. Theory Ser.  B 62 (1994), 63–95. DOI 10.1006/jctb.1994.1055 | MR 1290631
[2] R.  Fraïssé: Theory of Relations. North-Holland, Amsterdam, 1986. MR 0832435
[3] D.  Jakubíková-Studenovská: Homogeneous monounary algebras. Czechoslovak Math.  J. 52(127) (2002), 309–317. DOI 10.1023/A:1021722527256 | MR 1905437
[4] D.  Jakubíková-Studenovská: On homogeneous and 1-homogeneous monounary algebras. Contributions to General Algebra  12. Proceedings of the Wien Conference, June 1999, Verlag J. Heyn, 2000, pp. 221–224. MR 1777661
[5] D.  Jakubíková-Studenovská: On 2-homogeneity of monounary algebras. Czechoslovak Math.  J. 53(128) (2003), 55–68. DOI 10.1023/A:1022919307623 | MR 1961998
Partner of
EuDML logo