Internet is the main tool for accessing and disseminating information in the knowledge society, and human languages provide the basic support for such communication process. The Region of Madrid intends making knowledge the basis of its economic, social and human development. For this purpose, it is necessary developing and taking advantage of the impact of such communication channel. High leve...

We propose a homological approach to two conjectures descended from the Erdős-Ko-Rado Theorem, one due to Chvátal and the other to Frankl and Füredi. We apply the method to reprove, and in one case improve, results of these authors related to their conjectures.

We consider Erdős-Ko-Rado sets of generators in classical finite polar spaces. These are sets of generators that all intersect non-trivially. We characterize the Erdős-Ko-Rado sets of generators of maximum size in all polar spaces, except for H(4n+ 1, q) with n ≥ 2.

Creation of information society, or in other words, a society based on knowledge, has wide consequences, both on individual and complete society, and in general – on a economy of one country. Development and implementation of ICT represents a stimulant for economic growth. On individual level, knowledge, skills and information gathered using ICT, are expanding individual possibilities of person...

A set system is called t-intersecting if every two members meet each other in at least t elements. Katona determined the minimum ratio of the shadow and the size of such families and showed that the Erdős–Ko–Rado theorem immediately follows from this result. The aim of this note is to reproduce the proof to obtain a slight improvement in the Kneser graph. We also give a brief overview of corres...

Let k and m be positive integers. A collection of k-multisets from {1, . . . ,m} is intersecting if every pair of multisets from the collection is intersecting. We prove that for m ≥ k +1, the size of the largest such collection is ( m+k−2 k−1 ) and that when m > k + 1, only a collection of all the k-multisets containing a fixed element will attain this bound. The size and structure of the larg...

Chih-Ko Yeh,1,2 Tazuko K. Hymer,1 April L. Sousa,1 Bin-Xian Zhang,3,4 Meyer D. Lifschitz,3,4 and Michael S. Katz1,4 1Geriatric Research, Education and Clinical Center, and 3Research Service, South Texas Veterans Health Care System, Audie L. Murphy Division, San Antonio 78229-4404; and Departments of 2Dental Diagnostic Science and 4Medicine, University of Texas Health Science Center at San Anton...

A family of sets is t-intersecting if any two sets from the family contain at least t common elements. Given a t-intersecting family of r-sets from an n-set, how many distinct sets of size k can occur as pairwise intersections of its members? We prove an asymptotic upper bound on this number that can always be achieved. This result can be seen as a generalization of the Erdős-Ko-Rado theorem.

This paper is about inclusion in the prosperous “winner” networks and practices, caught by the term “knowledge society”. It tells about some people and a location in the Arctic rims of the European Union. The process presented can be described as enacted ambitions for knowledge society inclusion. Among the people involved there have been researchers and professionals of several different nation...

Life-long learning is a key issue for our knowledge society. With social software systems new heterogeneous kinds of technology enhanced informal learning are now available to the life-long learner. Learners outside of learning institutions now have access to powerful social communities of experts and peers who are together forging a new web 2.0. This paper reviews current work in pan-European ...