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2001, br. 5, str. 163-167
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On a family of (n + 1)-ary equivalence relations
(naslov ne postoji na srpskom)
aUniverzitet u Novom Sadu, Prirodno-matematički fakultet, Departman za matematiku i informatiku bUniverzitet u Kragujevcu, Tehnički fakultet, Čačak
e-adresa: zizo@tfc.kg.ac.yu
Ključne reči: partitions of type n; (n + 1)-ary equivalence relation
Sažetak
(ne postoji na srpskom)
The notation of a partition of type n, (n Є N), was introduced by J. Hartmanis in [1] as a generalization of the notion of an ordinary partition of a set. It is well-known fact that partitions Q (of type 1) correspond in an one-one way to equivalence relations on Q. In this article we introduce an analogous family of relations (Fn(Q)) for partitions of type n. Furthermore for p Є Fn(Q) the following statements hold: ○ (n+1 p) = p and (n p) - 1 = p for n = 1: ~ ○ ~ = ~ and ~ (cf. [3]). A similar family of relations for partitions of type n was described by H.E. Pickett in [2] point out the differences.
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Reference
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Hartmanis, J. (1961) Generalized partitions and lattice embedding theorems. u: Proc. of Symposia in Pure Mathematics, Amer. Math. Soc, vol. II, 22-30, Lattice theory
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Mal'cev, A.I. (1970) Algebraic systems. Moscow: Nauka, in Russian
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Pickett, H.E. (1966) A note on generalized equivalence relation. Amer. Math. Monthly, 73-8, 860-861
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