On lattices from combinatorial game theory modularity and a representation theorem: Finite case

We show that a self-generated set of combinatorial games, S, may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question “Is there a set which will give an on-distributive but modular lattice?” appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented.

Content analysis model to analyze facets of social mission of public library on the Facebook and in the websites

In this paper we present the development and the implementation of a content analysis model for observing aspects relating to the social mission of the public library on Facebook pages and websites. The model is unique and it was developed from the literature. There were designed the four categories for analysis Generate social capital and social cohesion, Consolidate democracy and citizenship, Social and digital inclusion and Fighting illiteracies. The model enabled the collection and the analysis of data applied to a case study consisting of 99 Portuguese public libraries with Facebook page. With this model of content analysis we observed the facets of social mission and we read the actions with social facets on the Facebook page and in the websites of public libraries. At the end we discuss in parallel the results of observation of the Facebook of libraries and the websites. By reading the description of the actions of the social mission, the general conclusion and the most immediate is that 99 public libraries on Facebook and websites rarely publish social character actions, and the results are little satisfying. The Portuguese public libraries highlight substantially the actions in the category Generate social capital and social cohesion.