La notion de tresse de Gutmann a été introduite ([4]) pour généraliser la notion de chaîne de Gutmann qui restait souvent assez loin du protocole observé. Les tresses de Gutmann ont été étudiées ([3], [4], [6]) en considérant que les réponses au questionnaire étaient dichotomiques. Nous supposons ici que les réponses aux questions appartiennent à un ensemble fini totalement ordonné quelconque.
Almost Distributive Lattices (ADL) are structures defined by Swamy and Rao [14] as a common abstraction of some generalizations of the Boolean algebra. In our paper, we deal with a certain further generalization of ADLs, namely the Generalized Almost Distributive Lattices (GADL). Our main aim was to give the formal counterpart of this structure and we succeeded formalizing all items from the Section 3 of Rao et al.’s paper [13]. Essentially among GADLs we can find structures which are neither V-commutative...
We denote by the class of all cardinals; put . Let be a class of algebraic systems. A generalized cardinal property on is defined to be a rule which assings to each an element of such that, whenever and , then . In this paper we are interested mainly in the cases when (i) is the class of all bounded lattices having more than one element, or (ii) is a class of lattice ordered groups.
In this paper we apply the notion of cell of a lattice for dealing with graph automorphisms of lattices (in connection with a problem proposed by G. Birkhoff).