Repository logo
 
Loading...
Project Logo
Research Project

Research in Economics and Mathematics

Authors

Publications

On lattices from combinatorial game theory: infinite case
Publication . Carvalho, Alda; Santos, Carlos; Dias, Cátia; Coelho, Francisco; Neto, João P.; Nowakowski, Richard; Vinagre, Sandra
Given a set of combinatorial games, the children are all those games that can be generated using as options the games of the original set. It is known that the partial order of the children of all games whose birthday is less than a fxed ordinal is a distributive lattice and also that the children of any set of games form a complete lat tice. We are interested in the converse. In a previous paper, we showed that for any fnite lattice there exists a fnite set of games such that the partial order of the chil dren, minus the top and bottom elements, is isomorphic to the original lattice. Here, the main part of the paper is to extend the result to infnite complete lattices. An original motivating question was to characterize those sets whose children generate distributive lattices. While we do not solve it, we show that if the process of taking children is iterated, eventually the corresponding lattice is distributive.

Organizational Units

Description

Keywords

Contributors

Funders

Funding agency

Fundação para a Ciência e a Tecnologia

Funding programme

6817 - DCRRNI ID

Funding Award Number

UIDB/05069/2020

ID