﻿<%@ Page Language="C#" MasterPageFile="~/Main.master" AutoEventWireup="true" Title="Volume7 Issue3" %>
Symmetric Operations on Equivalence Relations
Matteo Mainetti
Sirindhorn International Institute of Technology, Thammasat University, Patumthani 12121 Thailand
mainetti@siit.tu.ac.th
Annals of Combinatorics 7 (3) p.325-348 September, 2003
AMS Subject Classification: 05A18, 05C90, 03E02, 91D30
Abstract:
A new binary operation on the family of equivalence relations was introduced and studied by Britz, Mainetti, and Pezzoli. In this paper we give an equivalent, easier to grasp, definition of the same binary operation, and we prove it to be just an example of a bigger family of binary operations, which are shown to have interesting interpretation and meaning.
Keywords: equivalence relation, Jónsson type, trust graph

References:

1. T. Britz, M. Mainetti, and L. Pezzoli,Some operations on the family of equivalence relations, In: Algebraic Combinatorics and Computer Science, H. Crapo and D. Senato, Eds., Springer-Verlag, 2001, pp. 445–460.

2. M.-L. Dubreil-Jacotin and P. Dubreil, Théorie algébrique des relations d'équivalence, J. Mathématique 18 (1939) 63–95.

3. P. Dubreil, Relations binaires et applications, C. R. Acad. Sci. Paris 230 (1950) 1028–1030.

4. D. Finberg, M. Mainetti, and G.-C. Rota, The logic of commuting equivalence relations, In: Logic and Algebra, Lecture Notes in Pure and Applied mathematics, Vol. 180, A. Ursini and P. Aglian`o, Eds., Decker, 1996, pp. 69–96.

5. M. Haiman, Proof theory for linear lattices, Adv. Math. 58 (3) (1985) 209–242.

6. M. Haiman, Arguesian lattices which are not type-1, Algebra Universalis 28 (1) (1991) 128– 137.

7. G. Hutchinson, A complete logic for n-permutable congruence lattices, Algebra Universalis 13 (1981) 206–224.

8. B. Jónsson, On the representation of lattices, Math. Scand. 1 (1953) 193–206.

9. Ø. Ore, Theory of equivalence relations, Duke Math. J. 9 (1942) 573–627.